Problem

Source: Ukrainian mathematical olympiad 2018 10.4 and 11.3

Tags: functional equation, function, algebra



Find all functions $f:[0,+\infty) \mapsto [0,+\infty)$, which for all nonnegative $x,y$ satisfy $$f(f(x)+f(y))=xyf(x+y)$$ Proposed by Igor Voronovich