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Balkan MO 2017, problem3

Source: BMO 2017, problem 3

May 4, 2017
number theoryalgebra

Problem Statement

Let N\mathbb{N} denote the set of positive integers. Find all functions f:N⟶Nf:\mathbb{N}\longrightarrow\mathbb{N} such that n+f(m)∣f(n)+nf(m)n+f(m)\mid f(n)+nf(m) for all m,n∈Nm,n\in \mathbb{N}
Proposed by Dorlir Ahmeti, Albania
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