Determine all functions
Source: Austrian Mathematical Olympiad 2008 Problem 4
February 6, 2009
functionmodular arithmeticalgebra unsolvedalgebra
Problem Statement
Determine all functions mapping the set of positive integers to the set of non-negative integers satisfying the following conditions:
(1) f(mn) \equal{} f(m)\plus{}f(n),
(2) f(2008) \equal{} 0, and
(3) f(n) \equal{} 0 for all .