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Functional equation with sum of squares

Source: Macedonian Mathematical Olympiad 2023 P1

April 9, 2023
algebrafunctional equationMacedonianational olympiad

Problem Statement

Determine all functions f:R→Rf:\mathbb{R} \rightarrow \mathbb{R} such that for all x,y∈Rx,y \in \mathbb{R} we have: xf(x+y)+yf(y−x)=f(x2+y2) .xf(x+y)+yf(y-x) = f(x^2+y^2)\,. Proposed by Nikola Velov
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