Problem

Source: ELMO Shortlist 2012, A8

Tags: function, modular arithmetic, induction, algebra, functional equation, algebra proposed



Find all functions $f : \mathbb{Q} \to \mathbb{R}$ such that $f(x)f(y)f(x+y) = f(xy)(f(x) + f(y))$ for all $x,y\in\mathbb{Q}$. Sammy Luo and Alex Zhu.