Gazeta matematică 2012: Difference between revisions
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== Gazeta Matematică 9/2012 == | == Gazeta Matematică 9/2012 == | ||
'''E:14383 (Gheorghe Gherasim)''' | '''[[E:14383]] (Gheorghe Gherasim)''' | ||
''Numerele naturale distincte'' <math>a</math>'','' <math>b</math> ''verifică <math>9 \cdot [\,a, b]\,=a \cdot b \cdot (\,a \cdot b)\,</math>.'' | ''Numerele naturale distincte'' <math>a</math>'','' <math>b</math> ''verifică <math>9 \cdot [\,a, b]\,=a \cdot b \cdot (\,a \cdot b)\,</math>.'' | ||
Revision as of 16:34, 30 November 2024
Gazeta Matematică 9/2012
E:14383 (Gheorghe Gherasim)
Numerele naturale distincte 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} , 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} verifică 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 9 \cdot [\,a, b]\,=a \cdot b \cdot (\,a \cdot b)\,} .
i) Arătați că 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} 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 b} nu sunt prime între ele.
ii) Arătați că diferența numerelor este cel puțin 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 3} .
Se consideră că reprezintă cel mai mic multiplu comun al numerelor 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 b} , iar 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,b)} este cel mai mare divizor comun al numerelor 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} 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 b} .
![{\displaystyle [a,b]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9c4b788fc5c637e26ee98b45f89a5c08c85f7935)
E:14380 (Vasile Ienuțaș)
Determinați cifrele 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} 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 b} știind că 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{ab}=(a+b)(a+b-1)} .