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O problema de divizibilitate cu 7

 
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BogdanCNFB
Thales


Joined: 07 May 2008
Posts: 141
Location: Craiova

PostPosted: Wed May 14, 2008 1:42 pm    Post subject: O problema de divizibilitate cu 7 Reply with quote

Fie x,y\in Z astfel ca 7\mid x^3+x^2\cdot y+x\cdot y^2+y^3. Sa se arate ca 343\mid x^3+x^2\cdot y+x\cdot y^2+y^3.
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Beniamin Bogosel
Co-admin


Joined: 07 Mar 2008
Posts: 760
Location: Chambery, Franta

PostPosted: Wed May 14, 2008 6:18 pm    Post subject: Reply with quote

Incearca x=3,y=4. Atunci x^3+x^2y+xy^2+y^3=(x+y)(x^2+y^2)=175, care e divizibil cu 7 si nu e cu 343...
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moldovan ana
Pitagora


Joined: 23 Sep 2009
Posts: 68

PostPosted: Tue Feb 23, 2010 7:00 am    Post subject: Reply with quote

Este problema co4933 din GM n4/2008 care la solutie are erata dar si asa solutia data se contrazice cu ipoteza
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