E:16382: Difference between revisions
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''Afișați numerele întregi pozitive <math>\overline{abcd}</math> cu proprietatea''<math display="block">a^7 + e^d + ad = \overline{a000}.</math>'''Soluție''' | ''Afișați numerele întregi pozitive <math>\overline{abcd}</math> cu proprietatea''<math display="block">a^7 + e^d + ad = \overline{a000}.</math>'''Soluție''' | ||
Deoarece <math>4^7 > 9999</math> și <math>1^7 + a^b + a^c + a^d < 1000</math>, avem <math>a = 2</math> sau <math>a = 3</math>. | Deoarece <math>4^7 > 9999</math> și <math>1^7 + a^b + a^c + a^d < 1000</math>, avem <math>a = 2</math> sau <math>a = 3</math>. | ||
Revision as of 12:24, 16 January 2024
E:16382 (Cristina Vijdeluc și Mihai Vijdeluc)
Afișați numerele întregi pozitive Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \overline{abcd}} cu proprietateaFailed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a^7 + e^d + ad = \overline{a000}.} Soluție
Deoarece Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 4^7 > 9999}
și Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 1^7 + a^b + a^c + a^d < 1000}
, avem Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a = 2}
sau Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a = 3}
.
Egalitatea din enunț corespunde scrierii numărului Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \overline{a000}} în baza .
Cum Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 2000 = 11111010000_2} , Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a=2} nu convine.
De asemenea, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 3000 = 10101001000_2} corespunde egalității din enunț Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 3000 = 3^7 + 3^5 + 3^4 + 3^2 \cdot 2^2.} Prin urmare, avem soluțiile Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle b = 6} , Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle c = 4} , Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle d = 1} și permutările acestora.
Se obțin numerele întregi pozitive: Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \{{3641}, {3614}, {3461}, {3461}, {3164}, {3146}\}.}