The theorem is stated here: http://en.wikipedia.org/wiki/Fermat's_Last_Theorem
Fermat's Last Theorem...states that no three positive integers $a$, $b$, and $c$ can satisfy the equation $a^n$ + $b^n$ = $c^n$ for any integer value of n greater than two.
What is known about solutions for any non-zero integers $a$, $b$, and $c$, and any integer $n > 2$? (not just a restriction to only positive integers). Are there any solutions? If so, are there only finitely many? Infinitely many?