Problem

Source: Kosovo Math Olympiad 2025, Grade 11, Problem 2

Tags: functional equation, Reals, Kosovo, algebra



Find all functions $f:\mathbb{R}\rightarrow\mathbb{R}$ with the property that for every real numbers $x$ and $y$ it holds that $$f(x+yf(x+y))=f(x)+f(xy)+y^2.$$