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.
Problem
Source: Czech and Slovak Match 2000 P4
Tags: algebra, polynomial, Integer Polynomial, integer root
Source: Czech and Slovak Match 2000 P4
Tags: algebra, polynomial, Integer Polynomial, integer root
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.