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Turkey TST polynominal with integer coefficients

Source: Turkey TST 2009, Problem 4

April 5, 2009
algebrapolynomialabstract algebranumber theoryprime numbersalgebra unsolved

Problem Statement

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