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.  

We are considering the equation
$$
a^n + b^n = c^n.
$$
Clearly if $n$ is even, then negatives just go away, so let's say that $n$ is odd.
You have some cases. One case is where $a$ and $c$ are positive, but $b$ is negative. Then the equation is equivalent to $a^n = (-b)^n + c^n$. So this case isn't interesting. You also have the case where $a$ and $b$ are positive and $c$ is negative. But there clearly is not such solution. If all are negative we also don't get anything new.
Anyway, if you continue considering the different cases you will realize that the important case is where $a$, $b$, and $c$ are all positive.
As @quid says above, if you find a solution in the non-zero integers, then you will have a solution in the natural numbers.
