Prove that if $n$ is a square-free positive integer, there are no coprime positive integers $x$ and $y$ such that $(x + y)^3$ divides $x^n+y^n$
Source: Romania TST for BMO 1994,first problem
Tags: number theory
Prove that if $n$ is a square-free positive integer, there are no coprime positive integers $x$ and $y$ such that $(x + y)^3$ divides $x^n+y^n$