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Ecuatii in numere intregi

 
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Z
Euclid


Joined: 21 Apr 2009
Posts: 10

PostPosted: Fri Apr 24, 2009 8:33 pm    Post subject: Reply with quote

1. Pentru ce valori ale lui "n" numar natural si n>1 ecuatia 3x^n+4y^n=5z^n are solutii in multimea numerelor intregi diferite de zero si prime intre ele?

2. Pentru ce valori ale lui "a","b","c" numere intregi diferite de zero, prime intre ele si "n" numar natural ecuatia ax^n+by^n=cz^n are valori in multimea numerelor intregi?
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harrypham
Euclid


Joined: 18 Jul 2011
Posts: 24

PostPosted: Mon Jul 18, 2011 6:32 am    Post subject: Reply with quote

Can You post this Problem by English, thanks
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Laurian Filip
Site Admin


Joined: 25 Nov 2007
Posts: 469
Location: Bucuresti

PostPosted: Mon Jul 18, 2011 8:54 am    Post subject: Reply with quote

1. For what values of n>1, positive integer, the equation 3x^n+4y^n=5z^n has comprime (relatively prime) solutions in \mathbb{Z}^*X\mathbb{Z}^*X\mathbb{Z}^*?

2. For what values of a,b,c \in \mathbb{Z}^*, coprime and n\in\mathbb{Z}^*_+ the equation ax^n+by^n=cz^n has solutions in \mathbb{Z}X\mathbb{Z}X\mathbb{Z}
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