Question 14
Let $\mathbb{N}$ denote the set of positive integers. Determine all functions $f: \mathbb{N} \rightarrow \mathbb{N}$ with the following property: for all positive integers $m$ and $n$, the number $f(m)+f(n)-m n$ is nonzero and is a divisor of the number $m f(m)+n f(n)$.