MathDB
f(m, m+k) = f(m,k)

Source: Turkey TST 1989 - P1

September 11, 2013
functionalgorithmnumber theory proposednumber theory

Problem Statement

Let Z+\mathbb{Z}^+ denote the set of positive integers. Find all functions f:Z+×Z+→Z+f: \mathbb{Z}^+ \times \mathbb{Z}^+ \rightarrow \mathbb{Z}^+ such that
[*] f(m,m)=mf(m,m)=m [*] f(m,k)=f(k,m)f(m,k) = f(k,m) [*] f(m,m+k)=f(m,k)f(m, m+k) = f(m,k) , for each m,k∈Z+m,k \in \mathbb{Z}^+.
Back to ProblemsView on AoPS