Hosted by The Math Forum

Problem of the Week 967

An Unusual Multiplicative Function

_____________________________________________
MacPoW Home ||  Forum PoWs ||  Teachers' Place ||  Student Center ||  Search MacPoW
_____________________________________________

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.

[Privacy Policy] [Terms of Use]

_____________________________________
Home || The Math Library || Quick Reference || Search || Help 
_____________________________________

© 1994-2014 Drexel University. All rights reserved.
http://mathforum.org/
The Math Forum is a research and educational enterprise of the Drexel University School of Education.The Math Forum is a research and educational enterprise of the Drexel University School of Education.


26 September 2002