Suppose f is a function from positive integers to positive integers and f(2) = 2 f is increasing (m < n => f(m) < f(n)) f is multiplicative (f(m*n) = f(m)*f(n) when m and n have no common factor) Prove that f(3) = 3.

Suppose f is a function from positive integers to positive integers and

Prove that f(3) = 3.

Source: Crux Mathematicorum, Sept. 2002, from a St Petersburg contest.