Problem

Source: India IMOTC 2024 Day 3 Problem 3

Tags: functional equation, algebra



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