Question 183
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.
$$
\frac{a^{m}+b^{m}}{a^{n}+b^{n}}
$$
is an integer.