MathDB

Unique NT Function

Source: IMO SL 2018 N6

July 17, 2019

functionnumber theoryIMO Shortlist

Problem Statement

Let

f : \{ 1, 2, 3, \dots \} \to \{ 2, 3, \dots \}

be a function such that

f(m + n) | f(m) + f(n)

for all pairs

m,n

of positive integers. Prove that there exists a positive integer

c > 1

which divides all values of

f