TITLE: Fermat's Equation
QUESTION [5 upvotes]: Can somebody help me with this. I am trying to prove something from Fermat's equation.
Fermat's Equation $x^n + y^n = z^n$, where $x,y,z$ and $n$ are positive integers. His last theorem states that this equation has no solution if $n \geq3$.
I want to prove that if the equation has no solution if $n$ is prime or $n = 4$, then it must be true that it has no solution if $n \geq3$.

REPLY [10 votes]: Hint: If you had a solution to $x^n+y^n=z^n$, could you write it as a solution to either $a^p+b^p=c^p$ for some prime $p$ or as a solution to $a^4+b^4=c^4$? (You will only need the latter equation for a very special case. The first will suffice for most.)
Double hint: Factor $n$.