Effective tests for cyclotomic polynomials

Abstract

We present two efficient tests that determine if a given polynomial is cyclotomic, or is a product of cyclotomics. The first method uses the fact that all the roots of a cyclotomic polynomial are roots of unity, and the second the fact that the degree of a cyclotomic polynomial is a value of ϕ(n), for some n. We can also find the cyclotomic factors of any polynomial.