MathNet 2015-part-04 — 191 problems (EN–VI) Question 46

Find all functions $f: \mathbb{Z}_{\gt 0} \rightarrow \mathbb{Z}_{\gt 0}$ such that $f(1)=2$ and such that for all $m, n \in \mathbb{Z}_{\gt 0}$ it holds that $\min (2 m+2 n, f(m+n)+1)$ is divisible by $\max (f(m)+f(n), m+n)$.