Problem

Source: 2010 China South East Mathematical Olympiad

Tags: number theory unsolved, number theory



Let $a$ and $b$ be positive integers such that $1\leq a<b\leq 100$. If there exists a positive integer $k$ such that $ab|a^k+b^k$, we say that the pair $(a, b)$ is good. Determine the number of good pairs.