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, Ψm(x), and to write Ψm(x) as ratios of expressions in Tn(x). We also prove the relation Ψm(Tn(x)) = Ψn(Tm(x)) for m, n having the same prime divisors and use it to express Ψm(x) as a linear combination of Tn(x) for certain values of m.
Subject Classification: (2010):