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Functional Equation and Divisibility

Source: Indonesian MO (INAMO) 2020, Day 1, Problem 3, or APMO 2019 Problem 1

October 13, 2020
algebrafunctional equationAPMO2020DivisibilityIndonesia MOIndonesian MO

Problem Statement

The wording is just ever so slightly different, however the problem is identical.
Problem 3. Determine all functions f:Nā†’Nf: \mathbb{N} \to \mathbb{N} such that n2+f(n)f(m)n^2 + f(n)f(m) is a multiple of f(n)+mf(n) + m for all natural numbers m,nm, n.
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