For what positive integers $n$ are there positive rational, but not integer, numbers $a$ and $b$ such that both numbers $a + b$ and $a^n + b^n$ are integers?
Source:
Tags: number theory, Integers
For what positive integers $n$ are there positive rational, but not integer, numbers $a$ and $b$ such that both numbers $a + b$ and $a^n + b^n$ are integers?