MathDB

integer polynomial, f(a) = b, f(b) = a, f(x) = x has at most 1 integer root

Source: Norwegian Mathematical Olympiad 1997 - Abel Competition p4

February 11, 2020

algebrapolynomialIntegerInteger Polynomial

Problem Statement

Let

p(x)

be a polynomial with integer coefficients. Suppose that there exist different integers

a

and

b

such that

f(a) = b

and

f(b) = a

. Show that the equation

f(x) = x

has at most one integer solution.