MathDB

Polynomial

Source: ARO 2021 10.6

April 20, 2021

algebrapolynomial

Problem Statement

Given is a polynomial

P(x)

of degree

n>1

with real coefficients. The equation

P(P(P(x)))=P(x)

has

n^3

distinct real roots. Prove that these roots could be split into two groups with equal arithmetic mean.