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PAMO Problem 5: Functional equation

Source: 2021 Pan-African Mathematics Olympiad, Problem 5

May 24, 2021
algebrafunctional equationfunction

Problem Statement

Find all functions ff :: R→R\mathbb{R} \rightarrow \mathbb{R} such that ∀x,y∈R\forall x,y \in \mathbb{R} : (f(x)+y)(f(y)+x)=f(x2)+f(y2)+2f(xy)(f(x)+y)(f(y)+x)=f(x^2)+f(y^2)+2f(xy)
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