20070204, 18:09  #1 
May 2005
Argentina
2·3·31 Posts 
Fermat last theorem generalization
We know that the pythagorean triplets admits integer solutions. Example
Wiles probed Fermat's last theorem that says there are no integer solutions to the equation for What if we try with 3 summands like this: We can find integer solutions for like this one The question is is there integer solutions for ? More generally, for unknows is there an integer solution for unknows? 
20070204, 20:46  #2 
"Mark"
Apr 2003
Between here and the
1794_{16} Posts 
Check out http://euler.free.fr/

20070205, 16:00  #3  
Nov 2003
2^{2}×5×373 Posts 
Quote:
FLT is about integer points on *curves*. Your "generalization" asks about *surfaces*. There are more degrees of freedom. More appropriate generalizations would be to ask about integers points on (1) Twists of the Fermat curve. (2) Curves with *unequal* exponents. (3) Affine or general linear transforms of the curves. 

20070205, 17:43  #4  
Aug 2002
Buenos Aires, Argentina
2×3×223 Posts 
Quote:
x^{n} + y^{n} = 1. 

20070206, 00:36  #5  
Einyen
Dec 2003
Denmark
BA6_{16} Posts 
Quote:
From rogue's link: 2813001^{4}=2767624^{4}+1390400^{4}+673865^{4} (Allan MacLeod) 8707481^{4}=8332208^{4}+5507880^{4}+1705575^{4} (D.J. Bernstein) and many others. Last fiddled with by ATH on 20070206 at 00:36 

20070206, 00:43  #6  
May 2005
Argentina
272_{8} Posts 
Thanks you all for all the replys,
Quote:


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