MathDB

Standard Polynomial NT

Source: Indonesia National Math Olympiad 2022 Problem 2 (INAMO 2022/2)

October 4, 2022

algebrapolynomialnumber theoryIndonesiaIndonesia MO

Problem Statement

Let

P(x)

be a polynomial with integer coefficient such that

P(1) = 10

and

P(-1) = 22

. (a) Give an example of

P(x)

such that

P(x) = 0

has an integer root. (b) Suppose that

P(0) = 4

, prove that

P(x) = 0

does not have an integer root.