Question 21
It is known that no divisor of the positive integer $n$ other than 1 is a perfect square.
Prove that there do not exist coprime positive integers $x$ and $y$ such that $x^n + y^n$ is a multiple of $(x + y)^3$.
Prove that there do not exist coprime positive integers $x$ and $y$ such that $x^n + y^n$ is a multiple of $(x + y)^3$.