MathNet 2011 Question 95

Write $\mathbf N^*=\{0,1,2,3,\ldots\}$. Find all increasing functions $f:\mathbf N\to\mathbf N^*$ satisfying $f(2)=2$ and $f(nm)=f(n)+f(m)$ for all $n,m\in\mathbf N$.