TITLE: Correct statement of Fermat's Last Theorem
QUESTION [10 upvotes]: I'm looking at the wikipedia page on Fermat's Last Theorem
In the statement it requires $a,b,c$ to be positive integers.  Is that correct?  I always took it to be no solutions in non-zero integers.  But this wiki page makes a big deal out of the bases being positive.  Has some counter-example turned up using negative integers that I'm missing?  Otherwise, I think we should fix the wiki page.

REPLY [4 votes]: The person who had the best possible reason to think about the presentation of the conjecture is Andrew Wiles.  In his paper on Fermat's Last Theorem, the formulation is symmetrical and allows rational solutions: 

if $u^p + v^p + w^p = 0$ with $u,v,w$ rational and $p \geq 3$, then $uvw=0$.

It's interesting that he also chose to not use the traditional letters $x,y,z$ and $n$ for the variables in the problem.  His paper "buries the lede" by not giving the elementary form of FLT until the sixth page, and stays as far away as possible from the archetypal Diophantine form of FLT other than to mention he has proved it, and to quote Fermat's formulation in Latin below the dedication.