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f(n) | f(m) - n iff n | m for all n,m

Source: 2022 Dutch BxMO TST p1

December 3, 2022

number theoryfunctional

Problem Statement

Find all functions

f : Z_{>0} \to Z_{>0}

for which

f(n) | f(m) - n

if and only if

n | m

for all natural numbers

m

and

n