MathDB

Putnam 1963 A2

Source: Putnam 1963

May 1, 2022

Putnamfunctionnumber theoryrelatively primefunctional equation

Problem Statement

Let

f:\mathbb{N}\rightarrow \mathbb{N}

be a strictly increasing function such that

f(2)=2

and

f(mn)=f(m)f(n)

for every pair of relatively prime positive integers

m

and

n

. Prove that

f(n)=n

for every positive integer

n