BMO 2023 | Problem 1 - 10 May 2023 - Balkan Mathematical Olympiad

Problem 1.
Find all functions $f\colon \mathbb{R} \rightarrow \mathbb{R}$ such that for all $x,y \in \mathbb{R}$ ,
$xf(x+f(y))=(y-x)f(f(x)).$
North Macedonia