## Perfect Power Sum

#### Problem

Let $x$ and $y$ be positive whole numbers, and let $p$ be any odd prime.

It is well known that $x^3 + y^3$ is never equal to an odd prime.

But given that $n$ is a positive integer which contains an odd factor greater than one, prove that $x^n +y^n = p$ has no solutions.

Problem ID: 307 (20 Jan 2007) Difficulty: 4 Star