Question 15
Determine all functions $f$ mapping the integers to the integers with the following property: For any two (not necessarily different) numbers $m$ and $n$, $\text{gcd}(m, n)$ is a divisor of $f(m) + f(n)$. (Note that $\text{gcd}(m, n) = \text{gcd}(|m|, |n|)$ and $\text{gcd}(m, 0) = |m|$ holds for all integers $m$ and $n$.)