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Clean and Memorable Functional Equation with a Conceptual Solution

Source: 2021 ISL A8

July 12, 2022

algebrafunctional equationfunction

Problem Statement

Determine all functions

f: \mathbb{R} \rightarrow \mathbb{R}

that satisfy

(f(a)-f(b))(f(b)-f(c))(f(c)-f(a)) = f(ab^2+bc^2+ca^2) - f(a^2b+b^2c+c^2a)

for all real numbers

a

b

c

.
Proposed by Ankan Bhattacharya, USA