MathNet 2017-part-06 — 176 problems (EN–VI) Question 120

Let $N$ denote the set of all positive integers. Find all functions $f: N \rightarrow N$ such that for all $m, n \in N$, $f(m) + f(n) - mn \neq 0$ and $(f(m) + f(n) - mn)$ divides $(mf(m) + nf(n))$.