Correct statement of Fermat's Last Theorem 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.  

Suppose there is a solution in non-zero integers. If $n$ is even this immediately yields a soltution in positive integers. 
So suppose $n$ is odd. If all three are negative, we clearly also get a positve solution. So assume one is negative two possitive (two negative, one positive can be reduced to this multipliying by $-1$). Clearly it cannot be $c$ that is negative, so assume it is $a$ but then we get  $ b^n =c^n  -a^n = c^n + (-a)^n$ a positive solution.  
In brief, insisting on positve is irrelevant, there are no nono-zero solutions either. 
