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Problem of the Week 967
An Unusual Multiplicative Function
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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
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26 September 2002