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CIIM 2009 Problem 6

Source:

June 9, 2016
CIIM 2009CIIMundergraduate

Problem Statement

Let ϵ\epsilon be an nn-th root of the unity and suppose z=p(ϵ)z=p(\epsilon) is a real number where pp is some polinomial with integer coefficients. Prove there exists a polinomial qq with integer coefficients such that z=q(2cos⁡(2π/n))z=q(2\cos(2\pi/n)).
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