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
40th Balkan Mathematical Olympiad (BMO 2023)
40. Балканска Математичка Олимпијада (БMO 2023)