Find all pairs of positive integers for which there exist relatively prime integers and greater than such that is an integer.
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.
Source: Srednjoeuropska matematička olimpijada 2015, pojedinačno natjecanje, problem 4
Školjka 
for which there exist relatively prime integers 
and 
greater than 
such that 
is an integer.