Problem

Source: Turkey TST 2009, Problem 4

Tags: algebra, polynomial, abstract algebra, number theory, prime numbers, algebra unsolved



For which $ p$ prime numbers, there is an integer root of the polynominal $ 1 + p + Q(x^1)\cdot\ Q(x^2)\ldots\ Q(x^{2p - 2})$ such that $ Q(x)$ is a polynominal with integer coefficients?