Chebyshev polynomials and the minimal polynomial of cos(2π/n) (II)

Abstract

We present methods to write Tn (x), Chebyshev polynomials of the first kind, as a product of minimal polynomials of cos(2π/m) over integers, Ψ m (x), and to write Ψ m (x) as ratios of expressions in Tn (x). We also prove the relation Ψ m (Tn (x)) = Ψ n (Tm (x)) for m, n having the same prime divisors and use it to express Ψ m (x) as a linear combination of Tn (x) for certain values of m.