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We solve the open problem of Y. Z. Gürtaş of factoring polynomials, whereare Chebyshev polynomials of the second kind. While the factors ofwere known, the pattern of their mapping toandwas not, and it was intriguing. Each factor is a polynomial of the formwith integer coefficients whose roots are. We then consider the analogous problem for Chebyshev polynomials of the first kind by deriving a factorization of. This factorization enables the method used to solve the open problem to be applied to this one, resulting in a more direct proof.

Factoring Variants of Chebyshev Polynomials of the First and Second Kinds with Minimal Polynomials of cos(2 π / d )