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find all functions , a - f(b) | af(a) - bf(b)

Source: 2022 Austrian Federal Competition For Advanced Students, Part 2 p1

October 5, 2022

functionnumber theorydivides

Problem Statement

Find all functions

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

with

a - f(b) | af(a) - bf(b)

for all

a, b \in Z_{>0}

.
(Theresia Eisenkoelbl)