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Easy integer functional equation

Source: APMO 2019 P1

June 11, 2019
functionnumber theoryalgebrafunctional equationAPMO

Problem Statement

Let Z+\mathbb{Z}^+ be the set of positive integers. Determine all functions f:Z+ā†’Z+f : \mathbb{Z}^+\to\mathbb{Z}^+ such that a2+f(a)f(b)a^2+f(a)f(b) is divisible by f(a)+bf(a)+b for all positive integers a,ba,b.
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