Problem

Source: MEMO 2015, problem I-4.

Tags: number theory, relatively prime, Exponents, factorization, Euclidean algorithm



Find all pairs of positive integers $(m,n)$ for which there exist relatively prime integers $a$ and $b$ greater than $1$ such that $$\frac{a^m+b^m}{a^n+b^n}$$ is an integer.