Two simple remarks: The polynomial $ x^k-1$ can be factorised over the integers as a product of (irreducible) cyclotomic polynomials: $ $ x^k-1 = \prod_{d|k}\Phi_d(x).$ $ If we choose $ k$ to be a number that has a lot of divisors, then $ x^k-1$ will have a lot of factors. For example, if $ k$Read more