Problem

Source: Indonesia IMO 2007 TST, Stage 2, Test 5, Problem 2

Tags: function, algebra proposed, algebra



Find all functions $ f: \mathbb{R} \rightarrow \mathbb{R}$ satisfying \[ f(f(x + y)) = f(x + y) + f(x)f(y) - xy\]for all real numbers $x$ and $y$.