Problem

Source: BxMO 2023, Problem 1

Tags: BxMO, algebra



Find all functions $f\colon\mathbb{R}\to\mathbb{R}$ such that $(x-y)\bigl(f(x)+f(y)\bigr)\leqslant f\bigl(x^2-y^2\bigr)$ for all $x,y\in\mathbb{R}$.