Problem

Source: 2022 Saudi Arabia IMO TST 1.3

Tags: functional equation, functional, algebra



Find all non-constant functions $f : Q^+ \to Q^+$ satisfying the equation $$f(ab + bc + ca) =f(a)f(b) +f(b)f(c)+f(c)f(a)$$for all $a, b,c \in Q^+$ .