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Cute FE, but you all get 0

Source: India IMOTC 2024 Day 3 Problem 3

May 31, 2024
functional equationalgebra

Problem Statement

Find all functions f:R→Rf : \mathbb{R} \to \mathbb{R} such that for all real numbers a,b,ca, b, c, we have f(a+b+c)f(ab+bc+ca)−f(a)f(b)f(c)=f(a+b)f(b+c)f(c+a). f(a+b+c)f(ab+bc+ca) - f(a)f(b)f(c) = f(a+b)f(b+c)f(c+a).
Proposed by Mainak Ghosh and Rijul Saini
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