Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

IIRC, there was such a result as "there is no more than 1 non-trivial solution of $x^n+y^n=z^n$, if any", wasn't it? (IIRC, Siegel theorem implies that there are finitely many solutions for $n>3$; so it is the "no more than 1" part that is of particular interest).

Also, any reviews of pre-Wiles' results on Fermat's Last Theorem are appreciated.

share|improve this question
    
Would that be up to common factors? –  Henning Makholm Jul 29 '12 at 21:45
    
@HenningMakholm Yes. –  some_math Jul 29 '12 at 21:51
3  
Faltings' Theorem implies that for $n>3$, there are at most finitely many solutions. –  Keenan Kidwell Jul 29 '12 at 21:59
    
@HenningMakholm Yes... modulo IIRC, sorry. Precisely formulated result is the expected answer to my question. –  some_math Jul 29 '12 at 22:03
    
@KeenanKidwell What about "there are at most 1 solution"? Yes, I may incorrectly remember... but it seems to me, that I had read such a result. That result was specific to Fermat's Last Theorem, and not to any homogeneous polynomial. –  some_math Jul 29 '12 at 22:09

1 Answer 1

The Wikipedia article gives a good summary of pre-Wiles work. One highlight: In 1985, Leonard Adleman, Roger Heath-Brown and Étienne Fouvry proved that the first case of Fermat's Last Theorem holds for infinitely many odd primes $p$.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.