CMO 1969 Problem 8

Let $f$ be a function with the following properties:

1. $f(n)$ is defined for every positive integer $n$;
2. $f(n)$ is an integer;
3. $f(2)=2$;
4. $f(mn)=f(m)f(n)$ for all $m$ and $n$;
5. $f(m)>f(n)$ whenever $m>n$.

Prove that $f(n)=n$.