Problem

Source: XIII International Festival of Young Mathematicians Sozopol 2024, Theme for 10-12 grade

Tags: algebra, functional equation



Find all functions \( f:\mathbb{Z} \to \mathbb{Z} \) such that \[ f(x + f(y) - 2y) + f(f(y)) = f(x) \]for all integers \( x \) and \( y \).