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Functional equation on relative primes

Source: Austrian-Polish 2004, Problem 7

July 5, 2015
algebrafunctional equationrelatively primenumber theory

Problem Statement

Determine all functions f:Z+ā†’Zf:\mathbb{Z}^+\to \mathbb{Z} which satisfy the following condition for all pairs (x,y)(x,y) of relatively prime positive integers: f(x+y)=f(x+1)+f(y+1).f(x+y) = f(x+1) + f(y+1).
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