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f(m^2)+f(mf(n))=f(m+n)f(m)

Source: Mexico National Olympiad Mock Exam 2019 P3

October 15, 2019
functional equationalgebra

Problem Statement

Let Z\mathbb{Z} be the set of integers. Find all functions f:Z→Zf: \mathbb{Z}\rightarrow \mathbb{Z} such that, for any two integers m,nm, n, f(m2)+f(mf(n))=f(m+n)f(m).f(m^2)+f(mf(n))=f(m+n)f(m).
Proposed by Victor Domínguez and Pablo Valeriano
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