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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.

© Copyright 2002 Stan Wagon. Reproduced with permission.


26 September 2002