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	<id>https://wiki.universitas.ro/index.php?action=history&amp;feed=atom&amp;title=E%3A15694</id>
	<title>E:15694 - Revision history</title>
	<link rel="self" type="application/atom+xml" href="https://wiki.universitas.ro/index.php?action=history&amp;feed=atom&amp;title=E%3A15694"/>
	<link rel="alternate" type="text/html" href="https://wiki.universitas.ro/index.php?title=E:15694&amp;action=history"/>
	<updated>2026-05-03T06:30:37Z</updated>
	<subtitle>Revision history for this page on the wiki</subtitle>
	<generator>MediaWiki 1.42.1</generator>
	<entry>
		<id>https://wiki.universitas.ro/index.php?title=E:15694&amp;diff=10136&amp;oldid=prev</id>
		<title>Andrei.Horvat at 17:50, 17 July 2024</title>
		<link rel="alternate" type="text/html" href="https://wiki.universitas.ro/index.php?title=E:15694&amp;diff=10136&amp;oldid=prev"/>
		<updated>2024-07-17T17:50:49Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;en&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 17:50, 17 July 2024&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l7&quot;&gt;Line 7:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 7:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Dacă &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;b&amp;lt;/math&amp;gt; sunt cele două numere, &amp;lt;math&amp;gt;a &amp;gt; b&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c&amp;lt;/math&amp;gt; este câtul şi restul, atunci &amp;lt;math&amp;gt;a + b = 2020&amp;lt;/math&amp;gt; &amp;lt;math&amp;gt;(1)&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;a = b \cdot c + c&amp;lt;/math&amp;gt; &amp;lt;math&amp;gt;(2)&amp;lt;/math&amp;gt;, cu &amp;lt;math&amp;gt;c &amp;lt; b&amp;lt;/math&amp;gt;.  &lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Dacă &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;b&amp;lt;/math&amp;gt; sunt cele două numere, &amp;lt;math&amp;gt;a &amp;gt; b&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c&amp;lt;/math&amp;gt; este câtul şi restul, atunci &amp;lt;math&amp;gt;a + b = 2020&amp;lt;/math&amp;gt; &amp;lt;math&amp;gt;(1)&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;a = b \cdot c + c&amp;lt;/math&amp;gt; &amp;lt;math&amp;gt;(2)&amp;lt;/math&amp;gt;, cu &amp;lt;math&amp;gt;c &amp;lt; b&amp;lt;/math&amp;gt;.  &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Înlocuind pe &amp;lt;math&amp;gt;(2)&amp;lt;/math&amp;gt; în &amp;lt;math&amp;gt;(1)&amp;lt;/math&amp;gt; avem &amp;lt;math&amp;gt;b \cdot c + c + b = 2020&amp;lt;/math&amp;gt;, ceea ce conduce la &amp;lt;math&amp;gt;c(b + 1) + b + 1 = 2021&amp;lt;/math&amp;gt;, de unde se obține&amp;lt;math display=&quot;block&quot;&amp;gt;(b + 1)(c + 1) = 2021.&amp;lt;/math&amp;gt;Cum &amp;lt;math&amp;gt;2021 = 43 \cdot 47&amp;lt;/math&amp;gt; putem avea &amp;lt;math&amp;gt;b + 1 = 43&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c + 1 = 47&amp;lt;/math&amp;gt; sau &amp;lt;math&amp;gt;b + 1 = 47&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c + 1 = 43&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;lt;/math&amp;gt;. În primul caz &amp;lt;math&amp;gt;b = 42&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c = 46&amp;lt;/math&amp;gt;, care nu convine (avem condiţia &amp;lt;math&amp;gt;c &amp;lt; b&amp;lt;/math&amp;gt;). În al doilea caz &amp;lt;math&amp;gt;b = 46&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c = 42&amp;lt;/math&amp;gt;. Obţinem &amp;lt;math&amp;gt;a = 1974&lt;/del&gt;&amp;lt;/math&amp;gt;.  &lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Înlocuind pe &amp;lt;math&amp;gt;(2)&amp;lt;/math&amp;gt; în &amp;lt;math&amp;gt;(1)&amp;lt;/math&amp;gt; avem &amp;lt;math&amp;gt;b \cdot c + c + b = 2020&amp;lt;/math&amp;gt;, ceea ce conduce la &amp;lt;math&amp;gt;c(b + 1) + b + 1 = 2021&amp;lt;/math&amp;gt;, de unde se obține&amp;lt;math display=&quot;block&quot;&amp;gt;(b + 1)(c + 1) = 2021.&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Cum &amp;lt;math&amp;gt; 2021 = 43 \cdot 47&amp;lt;/math&amp;gt; putem avea &amp;lt;math&amp;gt; b + 1 = 43&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c + 1 = 47&amp;lt;/math&amp;gt; sau &amp;lt;math&amp;gt;b + 1 = 47&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c + 1 = 43&amp;lt;/math&amp;gt;.  &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Deci, numerele căutate sunt&amp;lt;math display=&quot;block&quot;&amp;gt;a=1974, b=46.&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;În primul caz avem &amp;lt;math&amp;gt;b = 42&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt; c = 46 &amp;lt;/math&amp;gt;, care nu convine (avem condiţia &amp;lt;math&amp;gt;c &amp;lt; b&amp;lt;/math&amp;gt;). &lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;În al doilea caz avem &amp;lt;math&amp;gt;b = 46&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c = 42&amp;lt;/math&amp;gt;. Obţinem &amp;lt;math&amp;gt;a = 1974&amp;lt;/math&amp;gt;. &lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Deci, numerele căutate sunt &amp;lt;math display=&quot;block&quot;&amp;gt;a=1974, b=46.&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Andrei.Horvat</name></author>
	</entry>
	<entry>
		<id>https://wiki.universitas.ro/index.php?title=E:15694&amp;diff=10135&amp;oldid=prev</id>
		<title>Andrei.Horvat at 17:45, 17 July 2024</title>
		<link rel="alternate" type="text/html" href="https://wiki.universitas.ro/index.php?title=E:15694&amp;diff=10135&amp;oldid=prev"/>
		<updated>2024-07-17T17:45:59Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;en&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 17:45, 17 July 2024&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l8&quot;&gt;Line 8:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 8:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Înlocuind pe &amp;lt;math&amp;gt;(2)&amp;lt;/math&amp;gt; în &amp;lt;math&amp;gt;(1)&amp;lt;/math&amp;gt; avem &amp;lt;math&amp;gt;b \cdot c + c + b = 2020&amp;lt;/math&amp;gt;, ceea ce conduce la &amp;lt;math&amp;gt;c(b + 1) + b + 1 = 2021&amp;lt;/math&amp;gt;, de unde se obține&amp;lt;math display=&amp;quot;block&amp;quot;&amp;gt;(b + 1)(c + 1) = 2021.&amp;lt;/math&amp;gt;Cum &amp;lt;math&amp;gt;2021 = 43 \cdot 47&amp;lt;/math&amp;gt; putem avea &amp;lt;math&amp;gt;b + 1 = 43&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c + 1 = 47&amp;lt;/math&amp;gt; sau &amp;lt;math&amp;gt;b + 1 = 47&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c + 1 = 43&amp;lt;/math&amp;gt;. În primul caz &amp;lt;math&amp;gt;b = 42&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c = 46&amp;lt;/math&amp;gt;, care nu convine (avem condiţia &amp;lt;math&amp;gt;c &amp;lt; b&amp;lt;/math&amp;gt;). În al doilea caz &amp;lt;math&amp;gt;b = 46&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c = 42&amp;lt;/math&amp;gt;. Obţinem &amp;lt;math&amp;gt;a = 1974&amp;lt;/math&amp;gt;.  &lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Înlocuind pe &amp;lt;math&amp;gt;(2)&amp;lt;/math&amp;gt; în &amp;lt;math&amp;gt;(1)&amp;lt;/math&amp;gt; avem &amp;lt;math&amp;gt;b \cdot c + c + b = 2020&amp;lt;/math&amp;gt;, ceea ce conduce la &amp;lt;math&amp;gt;c(b + 1) + b + 1 = 2021&amp;lt;/math&amp;gt;, de unde se obține&amp;lt;math display=&amp;quot;block&amp;quot;&amp;gt;(b + 1)(c + 1) = 2021.&amp;lt;/math&amp;gt;Cum &amp;lt;math&amp;gt;2021 = 43 \cdot 47&amp;lt;/math&amp;gt; putem avea &amp;lt;math&amp;gt;b + 1 = 43&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c + 1 = 47&amp;lt;/math&amp;gt; sau &amp;lt;math&amp;gt;b + 1 = 47&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c + 1 = 43&amp;lt;/math&amp;gt;. În primul caz &amp;lt;math&amp;gt;b = 42&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c = 46&amp;lt;/math&amp;gt;, care nu convine (avem condiţia &amp;lt;math&amp;gt;c &amp;lt; b&amp;lt;/math&amp;gt;). În al doilea caz &amp;lt;math&amp;gt;b = 46&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c = 42&amp;lt;/math&amp;gt;. Obţinem &amp;lt;math&amp;gt;a = 1974&amp;lt;/math&amp;gt;.  &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Deci, numerele căutate sunt&amp;lt;math display=&amp;quot;block&amp;quot;&amp;gt;a=1974, b=46.&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Deci, numerele căutate sunt&amp;lt;math display=&amp;quot;block&amp;quot;&amp;gt;a=1974, b=46.&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Andrei.Horvat</name></author>
	</entry>
	<entry>
		<id>https://wiki.universitas.ro/index.php?title=E:15694&amp;diff=10134&amp;oldid=prev</id>
		<title>Andrei.Horvat at 17:42, 17 July 2024</title>
		<link rel="alternate" type="text/html" href="https://wiki.universitas.ro/index.php?title=E:15694&amp;diff=10134&amp;oldid=prev"/>
		<updated>2024-07-17T17:42:48Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;en&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 17:42, 17 July 2024&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l7&quot;&gt;Line 7:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 7:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Dacă &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;b&amp;lt;/math&amp;gt; sunt cele două numere, &amp;lt;math&amp;gt;a &amp;gt; b&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c&amp;lt;/math&amp;gt; este câtul şi restul, atunci &amp;lt;math&amp;gt;a + b = 2020&amp;lt;/math&amp;gt; &amp;lt;math&amp;gt;(1)&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;a = b \cdot c + c&amp;lt;/math&amp;gt; &amp;lt;math&amp;gt;(2)&amp;lt;/math&amp;gt;, cu &amp;lt;math&amp;gt;c &amp;lt; b&amp;lt;/math&amp;gt;.  &lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Dacă &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;b&amp;lt;/math&amp;gt; sunt cele două numere, &amp;lt;math&amp;gt;a &amp;gt; b&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c&amp;lt;/math&amp;gt; este câtul şi restul, atunci &amp;lt;math&amp;gt;a + b = 2020&amp;lt;/math&amp;gt; &amp;lt;math&amp;gt;(1)&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;a = b \cdot c + c&amp;lt;/math&amp;gt; &amp;lt;math&amp;gt;(2)&amp;lt;/math&amp;gt;, cu &amp;lt;math&amp;gt;c &amp;lt; b&amp;lt;/math&amp;gt;.  &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Înlocuind pe &amp;lt;math&amp;gt;(2)&amp;lt;/math&amp;gt; în &amp;lt;math&amp;gt;(1)&amp;lt;/math&amp;gt; avem &amp;lt;math&amp;gt;b \cdot c + c + b = 2020&amp;lt;/math&amp;gt;, ceea ce conduce la &amp;lt;math&amp;gt;c(b + 1) + b + 1 = 2021&amp;lt;/math&amp;gt;, de unde se obține &amp;lt;math display=&quot;block&quot;&amp;gt;(b + 1)(c + 1) = 2021.&amp;lt;/math&amp;gt;Cum &amp;lt;math&amp;gt;2021 = 43 \cdot 47&amp;lt;/math&amp;gt; putem avea &amp;lt;math&amp;gt;b + 1 = 43&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c + 1 = 47&amp;lt;/math&amp;gt; sau &amp;lt;math&amp;gt;b + 1 = 47&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c + 1 = 43&amp;lt;/math&amp;gt;. În primul caz &amp;lt;math&amp;gt;b = 42&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c = 46&amp;lt;/math&amp;gt;, care nu convine (avem condiţia &amp;lt;math&amp;gt;c &amp;lt; b&amp;lt;/math&amp;gt;). În al doilea caz &amp;lt;math&amp;gt;b = 46&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c = 42&amp;lt;/math&amp;gt;. Obţinem &amp;lt;math&amp;gt;a = 1974&amp;lt;/math&amp;gt;.&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Înlocuind pe &amp;lt;math&amp;gt;(2)&amp;lt;/math&amp;gt; în &amp;lt;math&amp;gt;(1)&amp;lt;/math&amp;gt; avem &amp;lt;math&amp;gt;b \cdot c + c + b = 2020&amp;lt;/math&amp;gt;, ceea ce conduce la &amp;lt;math&amp;gt;c(b + 1) + b + 1 = 2021&amp;lt;/math&amp;gt;, de unde se obține&amp;lt;math display=&quot;block&quot;&amp;gt;(b + 1)(c + 1) = 2021.&amp;lt;/math&amp;gt;Cum &amp;lt;math&amp;gt;2021 = 43 \cdot 47&amp;lt;/math&amp;gt; putem avea &amp;lt;math&amp;gt;b + 1 = 43&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c + 1 = 47&amp;lt;/math&amp;gt; sau &amp;lt;math&amp;gt;b + 1 = 47&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c + 1 = 43&amp;lt;/math&amp;gt;. În primul caz &amp;lt;math&amp;gt;b = 42&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c = 46&amp;lt;/math&amp;gt;, care nu convine (avem condiţia &amp;lt;math&amp;gt;c &amp;lt; b&amp;lt;/math&amp;gt;). În al doilea caz &amp;lt;math&amp;gt;b = 46&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c = 42&amp;lt;/math&amp;gt;. Obţinem &amp;lt;math&amp;gt;a = 1974&amp;lt;/math&amp;gt;.  &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Deci, numerele căutate sunt&amp;lt;math display=&amp;quot;block&amp;quot;&amp;gt;a=1974, b=46.&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Deci, numerele căutate sunt&amp;lt;math display=&amp;quot;block&amp;quot;&amp;gt;a=1974, b=46.&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Andrei.Horvat</name></author>
	</entry>
	<entry>
		<id>https://wiki.universitas.ro/index.php?title=E:15694&amp;diff=8710&amp;oldid=prev</id>
		<title>Andrei.Horvat at 12:38, 30 December 2023</title>
		<link rel="alternate" type="text/html" href="https://wiki.universitas.ro/index.php?title=E:15694&amp;diff=8710&amp;oldid=prev"/>
		<updated>2023-12-30T12:38:47Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
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				&lt;tr class=&quot;diff-title&quot; lang=&quot;en&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 12:38, 30 December 2023&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l1&quot;&gt;Line 1:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 1:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&#039;&#039;&#039;E:15694 (Traian Covaciu&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;, Baia Mare&lt;/del&gt;)&#039;&#039;&#039;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&#039;&#039;&#039;E:15694 (Traian Covaciu)&#039;&#039;&#039;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#039;&amp;#039;Suma a două numere naturale  nenule este 2020. Dacă împărţim primul număr la al doilea, obţinem câtul egal cu restul. Aflaţi cele două numere.&amp;#039;&amp;#039;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#039;&amp;#039;Suma a două numere naturale  nenule este 2020. Dacă împărţim primul număr la al doilea, obţinem câtul egal cu restul. Aflaţi cele două numere.&amp;#039;&amp;#039;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l5&quot;&gt;Line 5:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 5:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#039;&amp;#039;&amp;#039;Soluție.&amp;#039;&amp;#039;&amp;#039;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#039;&amp;#039;&amp;#039;Soluție.&amp;#039;&amp;#039;&amp;#039;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Dacă &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;b&amp;lt;/math&amp;gt; sunt cele două numere, &amp;lt;math&amp;gt;a &amp;gt; b&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c&amp;lt;/math&amp;gt; este câtul şi restul, atunci &amp;lt;math&amp;gt;a + b = 2020&amp;lt;/math&amp;gt; &amp;lt;math&amp;gt;(1)&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;a = b \cdot c + c&amp;lt;/math&amp;gt; &amp;lt;math&amp;gt;(2)&amp;lt;/math&amp;gt;, cu &amp;lt;math&amp;gt;c &amp;lt; b&amp;lt;/math&amp;gt;. Înlocuind pe &amp;lt;math&amp;gt;(2)&amp;lt;/math&amp;gt; în &amp;lt;math&amp;gt;(1)&amp;lt;/math&amp;gt; avem &amp;lt;math&amp;gt;b \cdot c + c + b = 2020&amp;lt;/math&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;. sau &lt;/del&gt;&amp;lt;math&amp;gt;c(b + 1) + b + 1 = 2021&amp;lt;/math&amp;gt;, de unde &amp;lt;math&amp;gt;(b + 1)(c + 1) = 2021&amp;lt;/math&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;. &lt;/del&gt;Cum &amp;lt;math&amp;gt;2021 = 43 \cdot 47&amp;lt;/math&amp;gt; putem avea &amp;lt;math&amp;gt;b + 1 = 43&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c + 1 = 47&amp;lt;/math&amp;gt; sau &amp;lt;math&amp;gt;b + 1 = 47&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c + 1 = 43&amp;lt;/math&amp;gt;. În primul caz &amp;lt;math&amp;gt;b = 42&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c = 46&amp;lt;/math&amp;gt;, care nu convine (avem condiţia &amp;lt;math&amp;gt;c &amp;lt; b&amp;lt;/math&amp;gt;). În al doilea caz &amp;lt;math&amp;gt;b = 46&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c = 42&amp;lt;/math&amp;gt;. Obţinem &amp;lt;math&amp;gt;a = 1974&amp;lt;/math&amp;gt;.&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Dacă &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;b&amp;lt;/math&amp;gt; sunt cele două numere, &amp;lt;math&amp;gt;a &amp;gt; b&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c&amp;lt;/math&amp;gt; este câtul şi restul, atunci &amp;lt;math&amp;gt;a + b = 2020&amp;lt;/math&amp;gt; &amp;lt;math&amp;gt;(1)&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;a = b \cdot c + c&amp;lt;/math&amp;gt; &amp;lt;math&amp;gt;(2)&amp;lt;/math&amp;gt;, cu &amp;lt;math&amp;gt;c &amp;lt; b&amp;lt;/math&amp;gt;.  &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Înlocuind pe &amp;lt;math&amp;gt;(2)&amp;lt;/math&amp;gt; în &amp;lt;math&amp;gt;(1)&amp;lt;/math&amp;gt; avem &amp;lt;math&amp;gt;b \cdot c + c + b = 2020&amp;lt;/math&amp;gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;, ceea ce conduce la &lt;/ins&gt;&amp;lt;math&amp;gt;c(b + 1) + b + 1 = 2021&amp;lt;/math&amp;gt;, de unde &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;se obține &lt;/ins&gt;&amp;lt;math &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;display=&quot;block&quot;&lt;/ins&gt;&amp;gt;(b + 1)(c + 1) = 2021&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;.&lt;/ins&gt;&amp;lt;/math&amp;gt;Cum &amp;lt;math&amp;gt;2021 = 43 \cdot 47&amp;lt;/math&amp;gt; putem avea &amp;lt;math&amp;gt;b + 1 = 43&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c + 1 = 47&amp;lt;/math&amp;gt; sau &amp;lt;math&amp;gt;b + 1 = 47&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c + 1 = 43&amp;lt;/math&amp;gt;. În primul caz &amp;lt;math&amp;gt;b = 42&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c = 46&amp;lt;/math&amp;gt;, care nu convine (avem condiţia &amp;lt;math&amp;gt;c &amp;lt; b&amp;lt;/math&amp;gt;). În al doilea caz &amp;lt;math&amp;gt;b = 46&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c = 42&amp;lt;/math&amp;gt;. Obţinem &amp;lt;math&amp;gt;a = 1974&amp;lt;/math&amp;gt;.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Deci, numerele căutate sunt&amp;lt;math display=&quot;block&quot;&amp;gt;a=1974, b=46.&amp;lt;/math&amp;gt;&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Andrei.Horvat</name></author>
	</entry>
	<entry>
		<id>https://wiki.universitas.ro/index.php?title=E:15694&amp;diff=8574&amp;oldid=prev</id>
		<title>Fellner Arthur at 16:43, 27 December 2023</title>
		<link rel="alternate" type="text/html" href="https://wiki.universitas.ro/index.php?title=E:15694&amp;diff=8574&amp;oldid=prev"/>
		<updated>2023-12-27T16:43:23Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;en&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 16:43, 27 December 2023&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l5&quot;&gt;Line 5:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 5:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#039;&amp;#039;&amp;#039;Soluție.&amp;#039;&amp;#039;&amp;#039;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#039;&amp;#039;&amp;#039;Soluție.&amp;#039;&amp;#039;&amp;#039;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Dacă &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;b&amp;lt;/math&amp;gt; sunt cele două numere, &amp;lt;math&amp;gt;a &amp;gt; b&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c&amp;lt;/math&amp;gt; este câtul şi restul, atunci &amp;lt;math&amp;gt;a + b = 2020&amp;lt;/math&amp;gt; &amp;lt;math&amp;gt;(1)&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;a = b &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;* &lt;/del&gt;c + c&amp;lt;/math&amp;gt; &amp;lt;math&amp;gt;(2)&amp;lt;/math&amp;gt;, cu &amp;lt;math&amp;gt;c &amp;lt; b&amp;lt;/math&amp;gt;. Înlocuind pe &amp;lt;math&amp;gt;(2)&amp;lt;/math&amp;gt; în &amp;lt;math&amp;gt;(1)&amp;lt;/math&amp;gt; avem &amp;lt;math&amp;gt;b &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;* &lt;/del&gt;c + c + b = 2020&amp;lt;/math&amp;gt;. sau &amp;lt;math&amp;gt;c(b + 1) + b + 1 = 2021&amp;lt;/math&amp;gt;, de unde &amp;lt;math&amp;gt;(b + 1)(c + 1) = 2021&amp;lt;/math&amp;gt;. Cum &amp;lt;math&amp;gt;2021 = 43 &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;* &lt;/del&gt;47&amp;lt;/math&amp;gt; putem avea &amp;lt;math&amp;gt;b + 1 = 43&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c + 1 = 47&amp;lt;/math&amp;gt; sau &amp;lt;math&amp;gt;b + 1 = 47&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c + 1 = 43&amp;lt;/math&amp;gt;. În primul caz &amp;lt;math&amp;gt;b = 42&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c = 46&amp;lt;/math&amp;gt;, care nu convine (avem condiţia &amp;lt;math&amp;gt;c &amp;lt; b&amp;lt;/math&amp;gt;). În al doilea caz &amp;lt;math&amp;gt;b = 46&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c = 42&amp;lt;/math&amp;gt;. Obţinem &amp;lt;math&amp;gt;a = 1974&amp;lt;/math&amp;gt;.&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Dacă &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;b&amp;lt;/math&amp;gt; sunt cele două numere, &amp;lt;math&amp;gt;a &amp;gt; b&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c&amp;lt;/math&amp;gt; este câtul şi restul, atunci &amp;lt;math&amp;gt;a + b = 2020&amp;lt;/math&amp;gt; &amp;lt;math&amp;gt;(1)&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;a = b &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;\cdot &lt;/ins&gt;c + c&amp;lt;/math&amp;gt; &amp;lt;math&amp;gt;(2)&amp;lt;/math&amp;gt;, cu &amp;lt;math&amp;gt;c &amp;lt; b&amp;lt;/math&amp;gt;. Înlocuind pe &amp;lt;math&amp;gt;(2)&amp;lt;/math&amp;gt; în &amp;lt;math&amp;gt;(1)&amp;lt;/math&amp;gt; avem &amp;lt;math&amp;gt;b &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;\cdot &lt;/ins&gt;c + c + b = 2020&amp;lt;/math&amp;gt;. sau &amp;lt;math&amp;gt;c(b + 1) + b + 1 = 2021&amp;lt;/math&amp;gt;, de unde &amp;lt;math&amp;gt;(b + 1)(c + 1) = 2021&amp;lt;/math&amp;gt;. Cum &amp;lt;math&amp;gt;2021 = 43 &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;\cdot &lt;/ins&gt;47&amp;lt;/math&amp;gt; putem avea &amp;lt;math&amp;gt;b + 1 = 43&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c + 1 = 47&amp;lt;/math&amp;gt; sau &amp;lt;math&amp;gt;b + 1 = 47&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c + 1 = 43&amp;lt;/math&amp;gt;. În primul caz &amp;lt;math&amp;gt;b = 42&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c = 46&amp;lt;/math&amp;gt;, care nu convine (avem condiţia &amp;lt;math&amp;gt;c &amp;lt; b&amp;lt;/math&amp;gt;). În al doilea caz &amp;lt;math&amp;gt;b = 46&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c = 42&amp;lt;/math&amp;gt;. Obţinem &amp;lt;math&amp;gt;a = 1974&amp;lt;/math&amp;gt;.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Fellner Arthur</name></author>
	</entry>
	<entry>
		<id>https://wiki.universitas.ro/index.php?title=E:15694&amp;diff=8539&amp;oldid=prev</id>
		<title>Fellner Arthur at 12:58, 27 December 2023</title>
		<link rel="alternate" type="text/html" href="https://wiki.universitas.ro/index.php?title=E:15694&amp;diff=8539&amp;oldid=prev"/>
		<updated>2023-12-27T12:58:06Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;en&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 12:58, 27 December 2023&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l5&quot;&gt;Line 5:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 5:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#039;&amp;#039;&amp;#039;Soluție.&amp;#039;&amp;#039;&amp;#039;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#039;&amp;#039;&amp;#039;Soluție.&amp;#039;&amp;#039;&amp;#039;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Dacă &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;b&amp;lt;/math&amp;gt; sunt cele două numere, &amp;lt;math&amp;gt;a &amp;gt; b&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c&amp;lt;/math&amp;gt; este câtul şi restul, atunci &amp;lt;math&amp;gt;a + b = 2020 (1)&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;a = b * c + c &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt; &lt;/del&gt;(2)&amp;lt;/math&amp;gt;, cu &amp;lt;math&amp;gt;c &amp;lt; b&amp;lt;/math&amp;gt;. Înlocuind pe &amp;lt;math&amp;gt;(2)&amp;lt;/math&amp;gt; în &amp;lt;math&amp;gt;(1)&amp;lt;/math&amp;gt; avem &amp;lt;math&amp;gt;b * c + c + b = 2020&amp;lt;/math&amp;gt;. sau &amp;lt;math&amp;gt;c(b + 1) + b + 1 = 2021&amp;lt;/math&amp;gt;, de unde &amp;lt;math&amp;gt;(b + 1)(c + 1) = 2021&amp;lt;/math&amp;gt;. Cum &amp;lt;math&amp;gt;2021 = 43 * 47&amp;lt;/math&amp;gt; putem avea &amp;lt;math&amp;gt;b + 1 = 43&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c + 1 = 47&amp;lt;/math&amp;gt; sau &amp;lt;math&amp;gt;b + 1 = 47&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c + 1 = 43&amp;lt;/math&amp;gt;. În primul caz &amp;lt;math&amp;gt;b = 42&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c = 46&amp;lt;/math&amp;gt;, care nu convine (avem condiţia &amp;lt;math&amp;gt;c &amp;lt; b&amp;lt;/math&amp;gt;). În al doilea caz &amp;lt;math&amp;gt;b = 46&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c = 42&amp;lt;/math&amp;gt;. Obţinem &amp;lt;math&amp;gt;a = 1974&amp;lt;/math&amp;gt;.&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Dacă &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;b&amp;lt;/math&amp;gt; sunt cele două numere, &amp;lt;math&amp;gt;a &amp;gt; b&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c&amp;lt;/math&amp;gt; este câtul şi restul, atunci &amp;lt;math&amp;gt;a + b = 2020&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;lt;/math&amp;gt; &amp;lt;math&amp;gt;&lt;/ins&gt;(1)&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;a = b * c + c&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;lt;/math&amp;gt; &amp;lt;math&amp;gt;&lt;/ins&gt;(2)&amp;lt;/math&amp;gt;, cu &amp;lt;math&amp;gt;c &amp;lt; b&amp;lt;/math&amp;gt;. Înlocuind pe &amp;lt;math&amp;gt;(2)&amp;lt;/math&amp;gt; în &amp;lt;math&amp;gt;(1)&amp;lt;/math&amp;gt; avem &amp;lt;math&amp;gt;b * c + c + b = 2020&amp;lt;/math&amp;gt;. sau &amp;lt;math&amp;gt;c(b + 1) + b + 1 = 2021&amp;lt;/math&amp;gt;, de unde &amp;lt;math&amp;gt;(b + 1)(c + 1) = 2021&amp;lt;/math&amp;gt;. Cum &amp;lt;math&amp;gt;2021 = 43 * 47&amp;lt;/math&amp;gt; putem avea &amp;lt;math&amp;gt;b + 1 = 43&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c + 1 = 47&amp;lt;/math&amp;gt; sau &amp;lt;math&amp;gt;b + 1 = 47&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c + 1 = 43&amp;lt;/math&amp;gt;. În primul caz &amp;lt;math&amp;gt;b = 42&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c = 46&amp;lt;/math&amp;gt;, care nu convine (avem condiţia &amp;lt;math&amp;gt;c &amp;lt; b&amp;lt;/math&amp;gt;). În al doilea caz &amp;lt;math&amp;gt;b = 46&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c = 42&amp;lt;/math&amp;gt;. Obţinem &amp;lt;math&amp;gt;a = 1974&amp;lt;/math&amp;gt;.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Fellner Arthur</name></author>
	</entry>
	<entry>
		<id>https://wiki.universitas.ro/index.php?title=E:15694&amp;diff=8538&amp;oldid=prev</id>
		<title>Fellner Arthur at 12:56, 27 December 2023</title>
		<link rel="alternate" type="text/html" href="https://wiki.universitas.ro/index.php?title=E:15694&amp;diff=8538&amp;oldid=prev"/>
		<updated>2023-12-27T12:56:59Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;en&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 12:56, 27 December 2023&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l5&quot;&gt;Line 5:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 5:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#039;&amp;#039;&amp;#039;Soluție.&amp;#039;&amp;#039;&amp;#039;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#039;&amp;#039;&amp;#039;Soluție.&amp;#039;&amp;#039;&amp;#039;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Dacă &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;b&amp;lt;/math&amp;gt; sunt cele două numere, &amp;lt;math&amp;gt;a &amp;gt; b&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c&amp;lt;/math&amp;gt; este câtul şi restul, atunci &amp;lt;math&amp;gt;a + b = 2020 (1)&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;a = b * c + c (2)&amp;lt;/math&amp;gt;, cu &amp;lt;math&amp;gt;c &amp;lt; b&amp;lt;/math&amp;gt;. Înlocuind pe &amp;lt;math&amp;gt;(2)&amp;lt;/math&amp;gt; în &amp;lt;math&amp;gt;(1)&amp;lt;/math&amp;gt; avem &amp;lt;math&amp;gt;b * c + c + b = 2020&amp;lt;/math&amp;gt;. sau &amp;lt;math&amp;gt;c(b + 1) + b + 1 = 2021&amp;lt;/math&amp;gt;, de unde &amp;lt;math&amp;gt;(b + 1)(c + 1) = 2021&amp;lt;/math&amp;gt;. Cum &amp;lt;math&amp;gt;2021 = 43 * 47&amp;lt;/math&amp;gt; putem avea &amp;lt;math&amp;gt;b + 1 = 43&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c + 1 = 47&amp;lt;/math&amp;gt; sau &amp;lt;math&amp;gt;b + 1 = 47&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c + 1 = 43&amp;lt;/math&amp;gt;. În primul caz &amp;lt;math&amp;gt;b = 42&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c = 46&amp;lt;/math&amp;gt;, care nu convine (avem condiţia &amp;lt;math&amp;gt;c &amp;lt; b&amp;lt;/math&amp;gt;). În al doilea caz &amp;lt;math&amp;gt;b = 46&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c = 42&amp;lt;/math&amp;gt;. Obţinem &amp;lt;math&amp;gt;a = 1974&amp;lt;/math&amp;gt;.&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Dacă &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;b&amp;lt;/math&amp;gt; sunt cele două numere, &amp;lt;math&amp;gt;a &amp;gt; b&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c&amp;lt;/math&amp;gt; este câtul şi restul, atunci &amp;lt;math&amp;gt;a + b = 2020 (1)&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;a = b * c + c &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt; &lt;/ins&gt;(2)&amp;lt;/math&amp;gt;, cu &amp;lt;math&amp;gt;c &amp;lt; b&amp;lt;/math&amp;gt;. Înlocuind pe &amp;lt;math&amp;gt;(2)&amp;lt;/math&amp;gt; în &amp;lt;math&amp;gt;(1)&amp;lt;/math&amp;gt; avem &amp;lt;math&amp;gt;b * c + c + b = 2020&amp;lt;/math&amp;gt;. sau &amp;lt;math&amp;gt;c(b + 1) + b + 1 = 2021&amp;lt;/math&amp;gt;, de unde &amp;lt;math&amp;gt;(b + 1)(c + 1) = 2021&amp;lt;/math&amp;gt;. Cum &amp;lt;math&amp;gt;2021 = 43 * 47&amp;lt;/math&amp;gt; putem avea &amp;lt;math&amp;gt;b + 1 = 43&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c + 1 = 47&amp;lt;/math&amp;gt; sau &amp;lt;math&amp;gt;b + 1 = 47&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c + 1 = 43&amp;lt;/math&amp;gt;. În primul caz &amp;lt;math&amp;gt;b = 42&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c = 46&amp;lt;/math&amp;gt;, care nu convine (avem condiţia &amp;lt;math&amp;gt;c &amp;lt; b&amp;lt;/math&amp;gt;). În al doilea caz &amp;lt;math&amp;gt;b = 46&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c = 42&amp;lt;/math&amp;gt;. Obţinem &amp;lt;math&amp;gt;a = 1974&amp;lt;/math&amp;gt;.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Fellner Arthur</name></author>
	</entry>
	<entry>
		<id>https://wiki.universitas.ro/index.php?title=E:15694&amp;diff=8537&amp;oldid=prev</id>
		<title>Fellner Arthur at 12:56, 27 December 2023</title>
		<link rel="alternate" type="text/html" href="https://wiki.universitas.ro/index.php?title=E:15694&amp;diff=8537&amp;oldid=prev"/>
		<updated>2023-12-27T12:56:38Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;en&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 12:56, 27 December 2023&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l5&quot;&gt;Line 5:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 5:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#039;&amp;#039;&amp;#039;Soluție.&amp;#039;&amp;#039;&amp;#039;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#039;&amp;#039;&amp;#039;Soluție.&amp;#039;&amp;#039;&amp;#039;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Dacă &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;b&amp;lt;/math&amp;gt; sunt cele două numere, &amp;lt;math&amp;gt;a &amp;gt; b&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c&amp;lt;/math&amp;gt; este câtul şi restul, atunci &amp;lt;math&amp;gt;a + b = 2020&amp;lt;/math&amp;gt; &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;(1) &lt;/del&gt;şi &amp;lt;math&amp;gt;a = b * c + c&amp;lt;/math&amp;gt; &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;(2)&lt;/del&gt;, cu &amp;lt;math&amp;gt;c &amp;lt; b&amp;lt;/math&amp;gt;. Înlocuind pe &amp;lt;math&amp;gt;(2)&amp;lt;/math&amp;gt; în &amp;lt;math&amp;gt;(1)&amp;lt;/math&amp;gt; avem &amp;lt;math&amp;gt;b * c + c + b = 2020&amp;lt;/math&amp;gt;. sau &amp;lt;math&amp;gt;c(b + 1) + b + 1 = 2021&amp;lt;/math&amp;gt;, de unde &amp;lt;math&amp;gt;(b + 1)(c + 1) = 2021&amp;lt;/math&amp;gt;. Cum &amp;lt;math&amp;gt;2021 = 43 * 47&amp;lt;/math&amp;gt; putem avea &amp;lt;math&amp;gt;b + 1 = 43&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c + 1 = 47&amp;lt;/math&amp;gt; sau &amp;lt;math&amp;gt;b + 1 = 47&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c + 1 = 43&amp;lt;/math&amp;gt;. În primul caz &amp;lt;math&amp;gt;b = 42&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c = 46&amp;lt;/math&amp;gt;, care nu convine (avem condiţia &amp;lt;math&amp;gt;c &amp;lt; b&amp;lt;/math&amp;gt;). În al doilea caz &amp;lt;math&amp;gt;b = 46&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c = 42&amp;lt;/math&amp;gt;. Obţinem &amp;lt;math&amp;gt;a = 1974&amp;lt;/math&amp;gt;.&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Dacă &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;b&amp;lt;/math&amp;gt; sunt cele două numere, &amp;lt;math&amp;gt;a &amp;gt; b&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c&amp;lt;/math&amp;gt; este câtul şi restul, atunci &amp;lt;math&amp;gt;a + b = 2020 &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;(1)&lt;/ins&gt;&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;a = b * c + c &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;(2)&lt;/ins&gt;&amp;lt;/math&amp;gt;, cu &amp;lt;math&amp;gt;c &amp;lt; b&amp;lt;/math&amp;gt;. Înlocuind pe &amp;lt;math&amp;gt;(2)&amp;lt;/math&amp;gt; în &amp;lt;math&amp;gt;(1)&amp;lt;/math&amp;gt; avem &amp;lt;math&amp;gt;b * c + c + b = 2020&amp;lt;/math&amp;gt;. sau &amp;lt;math&amp;gt;c(b + 1) + b + 1 = 2021&amp;lt;/math&amp;gt;, de unde &amp;lt;math&amp;gt;(b + 1)(c + 1) = 2021&amp;lt;/math&amp;gt;. Cum &amp;lt;math&amp;gt;2021 = 43 * 47&amp;lt;/math&amp;gt; putem avea &amp;lt;math&amp;gt;b + 1 = 43&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c + 1 = 47&amp;lt;/math&amp;gt; sau &amp;lt;math&amp;gt;b + 1 = 47&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c + 1 = 43&amp;lt;/math&amp;gt;. În primul caz &amp;lt;math&amp;gt;b = 42&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c = 46&amp;lt;/math&amp;gt;, care nu convine (avem condiţia &amp;lt;math&amp;gt;c &amp;lt; b&amp;lt;/math&amp;gt;). În al doilea caz &amp;lt;math&amp;gt;b = 46&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c = 42&amp;lt;/math&amp;gt;. Obţinem &amp;lt;math&amp;gt;a = 1974&amp;lt;/math&amp;gt;.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Fellner Arthur</name></author>
	</entry>
	<entry>
		<id>https://wiki.universitas.ro/index.php?title=E:15694&amp;diff=8536&amp;oldid=prev</id>
		<title>Fellner Arthur at 12:55, 27 December 2023</title>
		<link rel="alternate" type="text/html" href="https://wiki.universitas.ro/index.php?title=E:15694&amp;diff=8536&amp;oldid=prev"/>
		<updated>2023-12-27T12:55:42Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;en&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 12:55, 27 December 2023&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l5&quot;&gt;Line 5:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 5:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#039;&amp;#039;&amp;#039;Soluție.&amp;#039;&amp;#039;&amp;#039;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#039;&amp;#039;&amp;#039;Soluție.&amp;#039;&amp;#039;&amp;#039;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Dacă &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;b&amp;lt;/math&amp;gt; sunt cele două numere, &amp;lt;math&amp;gt;a &amp;gt; b&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c&amp;lt;/math&amp;gt; este câtul şi restul, atunci &amp;lt;math&amp;gt;a + b = 2020&amp;lt;/math&amp;gt; (1) şi &amp;lt;math&amp;gt;a = b * c + c&amp;lt;/math&amp;gt; (2), cu &amp;lt;math&amp;gt;c &amp;lt; b&amp;lt;/math&amp;gt;. Înlocuind pe (2) în (1) avem &amp;lt;math&amp;gt;b * c + c + b = 2020&amp;lt;/math&amp;gt;. sau &amp;lt;math&amp;gt;c(b + 1) + b + 1 = 2021&amp;lt;/math&amp;gt;, de unde &amp;lt;math&amp;gt;(b + 1)(c + 1) = 2021&amp;lt;/math&amp;gt;. Cum &amp;lt;math&amp;gt;2021 = 43 * 47&amp;lt;/math&amp;gt; putem avea &amp;lt;math&amp;gt;b + 1 = 43&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c + 1 = 47&amp;lt;/math&amp;gt; sau &amp;lt;math&amp;gt;b + 1 = 47&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c + 1 = 43&amp;lt;/math&amp;gt;. În primul caz &amp;lt;math&amp;gt;b = 42&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c = 46&amp;lt;/math&amp;gt;, care nu convine (avem condiţia &amp;lt;math&amp;gt;c &amp;lt; b&amp;lt;/math&amp;gt;). În al doilea caz &amp;lt;math&amp;gt;b = 46&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c = 42&amp;lt;/math&amp;gt;. Obţinem &amp;lt;math&amp;gt;a = 1974&amp;lt;/math&amp;gt;.&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Dacă &amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;b&amp;lt;/math&amp;gt; sunt cele două numere, &amp;lt;math&amp;gt;a &amp;gt; b&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c&amp;lt;/math&amp;gt; este câtul şi restul, atunci &amp;lt;math&amp;gt;a + b = 2020&amp;lt;/math&amp;gt; (1) şi &amp;lt;math&amp;gt;a = b * c + c&amp;lt;/math&amp;gt; (2), cu &amp;lt;math&amp;gt;c &amp;lt; b&amp;lt;/math&amp;gt;. Înlocuind pe &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;lt;math&amp;gt;&lt;/ins&gt;(2)&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;lt;/math&amp;gt; &lt;/ins&gt;în &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;lt;math&amp;gt;&lt;/ins&gt;(1)&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;lt;/math&amp;gt; &lt;/ins&gt;avem &amp;lt;math&amp;gt;b * c + c + b = 2020&amp;lt;/math&amp;gt;. sau &amp;lt;math&amp;gt;c(b + 1) + b + 1 = 2021&amp;lt;/math&amp;gt;, de unde &amp;lt;math&amp;gt;(b + 1)(c + 1) = 2021&amp;lt;/math&amp;gt;. Cum &amp;lt;math&amp;gt;2021 = 43 * 47&amp;lt;/math&amp;gt; putem avea &amp;lt;math&amp;gt;b + 1 = 43&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c + 1 = 47&amp;lt;/math&amp;gt; sau &amp;lt;math&amp;gt;b + 1 = 47&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c + 1 = 43&amp;lt;/math&amp;gt;. În primul caz &amp;lt;math&amp;gt;b = 42&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c = 46&amp;lt;/math&amp;gt;, care nu convine (avem condiţia &amp;lt;math&amp;gt;c &amp;lt; b&amp;lt;/math&amp;gt;). În al doilea caz &amp;lt;math&amp;gt;b = 46&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;c = 42&amp;lt;/math&amp;gt;. Obţinem &amp;lt;math&amp;gt;a = 1974&amp;lt;/math&amp;gt;.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Fellner Arthur</name></author>
	</entry>
	<entry>
		<id>https://wiki.universitas.ro/index.php?title=E:15694&amp;diff=8535&amp;oldid=prev</id>
		<title>Fellner Arthur at 12:51, 27 December 2023</title>
		<link rel="alternate" type="text/html" href="https://wiki.universitas.ro/index.php?title=E:15694&amp;diff=8535&amp;oldid=prev"/>
		<updated>2023-12-27T12:51:49Z</updated>

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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 12:51, 27 December 2023&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l1&quot;&gt;Line 1:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 1:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&#039;&#039;&#039;E:15694(Traian Covaciu, Baia Mare)&#039;&#039;&#039;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&#039;&#039;&#039;E:15694 (Traian Covaciu, Baia Mare)&#039;&#039;&#039;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#039;&amp;#039;Suma a două numere naturale  nenule este 2020. Dacă împărţim primul număr la al doilea, obţinem câtul egal cu restul. Aflaţi cele două numere.&amp;#039;&amp;#039;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#039;&amp;#039;Suma a două numere naturale  nenule este 2020. Dacă împărţim primul număr la al doilea, obţinem câtul egal cu restul. Aflaţi cele două numere.&amp;#039;&amp;#039;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Fellner Arthur</name></author>
	</entry>
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