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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

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