Problem

Source: Turkey IMO TST 2016 P5

Tags: function, number theory, functional equation, Divisibility



Find all functions $f: \mathbb{N} \to \mathbb{N}$ such that for all $m,n \in \mathbb{N}$ holds $f(mn)=f(m)f(n)$ and $m+n \mid f(m)+f(n)$ .