ISL 2013 N1

Let $\mathbb{Z}_{>0}$ be the set of positive integers. Find all functions $f: \mathbb{Z}_{>0} \rightarrow \mathbb{Z}_{>0}$ such that $$m^{2}+f(n) \mid m f(m)+n$$ for all positive integers $m$ and $n$. (Malaysia)