Factorization of cyclotomic polynomial values at Mersenne primes

TL;DR

This paper investigates the factorization properties of cyclotomic polynomial values at Mersenne primes over finite fields, providing new insights into their algebraic structure and related divisor sums.

Contribution

It introduces novel results on the factorization of cyclotomic polynomial values at Mersenne primes and enhances understanding of divisor sum factorizations in this context.

Findings

Factorization patterns of $\

Insights into the structure of cyclotomic polynomial values at Mersenne primes

Connections between polynomial factorization and divisor sum properties

Abstract

We get some results about the factorization of $\phi_p(M) \in {\mathbb{F}}_2[x]$, where $p$ is a prime number, $\phi_p$ is the corresponding cyclotomic polynomial and $M$ is a Mersenne prime (polynomial). By the way, we better understand the factorization of the sum of the divisors of $M^{2h}$, for a positive integer $h$.