Problem of the Week 967

An Unusual Multiplicative Function

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.

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