Factorization of Cyclotomic Polynomial Values at Mersenne Prime Polynomials

We present new results about the factorization of p(M ) F2[x], where p is a prime number, p is the corresponding cyclotomic polynomial, and M is a Mersenne prime polynomial.In particular, these results improve our understanding of the factorization of the sum of the divisors of M 2h for a positive integer h.This is related to the fixed points of the sum of divisors function on F2[x].The factorization of composed polynomials over finite fields is not well understood, and classical results on cyclotomic polynomials primarily concern the special case where M is replaced by x.