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IMO Shortlist 2013, Number Theory #1

Source: IMO Shortlist 2013, Number Theory #1

July 10, 2014
number theoryalgebrafunctional equationIMO Shortlist

Problem Statement

Let Z>0\mathbb{Z} _{>0} be the set of positive integers. Find all functions f:Z>0→Z>0f: \mathbb{Z} _{>0}\rightarrow \mathbb{Z} _{>0} such that m2+f(n)∣mf(m)+n m^2 + f(n) \mid mf(m) +n for all positive integers mm and nn.
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