Resultants of minimal polynomials of maximal real cyclotomic extensions

Define the n  th real cyclotomic polynomial to be the minimal polynomial over ZZ of ζn+ζn−1, where ζn=e2πi/nζn=e2πi/n is a primitive nth root of unity. We prove that the real cyclotomic polynomials can be formed from compositions of polynomials closely related to the Chebyshev polynomials of the first kind. We use these relations to determine the resultant of two real cyclotomic polynomials.