Question 99
Find all functions $f : \mathbb{R} \to \mathbb{R}$ such that
$$
f(xy + f(y)) f(x) = x^2 f(y) + f(xy)
$$
holds for all real numbers $x, y$.
$$
f(xy + f(y)) f(x) = x^2 f(y) + f(xy)
$$
holds for all real numbers $x, y$.
MathNet 2023-part-06 — 191 problems (EN–VI) Question 99
Math Olympiad Vault · MathNet 2023-part-06 — 191 problems (EN–VI)