PAMO 2003 Problem 1

Let $N_0=\{0, 1, 2 \cdots \}$ . Find all functions: $N_0 \to N_0$ such that:

(1) $f(n) < f(n+1)$ , all $n \in N_0$ ;

(2) $f(2)=2$ ;

(3) $f(mn)=f(m)f(n)$ , all $m, n \in N_0$ .