MathDB

P(x^4)P(x^3)P(x^2)P(x)+1 has no integer roots

Source: Czech and Slovak Match 2000 P4

October 1, 2017

algebrapolynomialInteger Polynomialinteger root

Problem Statement

Let

P(x)

be a polynomial with integer coefficients. Prove that the polynomial

Q(x) = P(x^4)P(x^3)P(x^2)P(x)+1

has no integer roots.