MathDB

Generalization of SL 2002 A3

Source: HMMT Invitational Contest 2016, Problem 4

April 22, 2016

HMICHMMTalgebrapolynomialInteger Polynomial

Problem Statement

Let

P

be an odd-degree integer-coefficient polynomial. Suppose that

xP(x)=yP(y)

for infinitely many pairs

x,y

of integers with

x\ne y

. Prove that the equation

P(x)=0

has an integer root.
Victor Wang