Question 124
Determine all functions $f: \mathbb{R} \to \mathbb{R}$ such that for any $x, y \in \mathbb{R}$ it holds that
$$
x f(x+y) + y f(y-x) = f(x^2 + y^2).
$$
$$
x f(x+y) + y f(y-x) = f(x^2 + y^2).
$$
MathNet 2023-part-04 — 191 problems (EN–VI) Question 124
Math Olympiad Vault · MathNet 2023-part-04 — 191 problems (EN–VI)