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f(ab + bc + ca) =f(a)f(b) +f(b)f(c)+f(c)f(a) in Q^+

Source: 2022 Saudi Arabia IMO TST 1.3

November 1, 2022
functional equationfunctionalalgebra

Problem Statement

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