Divisibility criteria and coefficient formulas for cyclotomic polynomials
Number Theory
2025-08-06 v1
Abstract
We establish necessary and sufficient conditions for a polynomial to be divisible by a cyclotomic polynomials and derive new formulas involving Ramanujan sums as an application of our results. Additionally, we provide new insights into the coefficients of cyclotomic polynomials and we propose a recursive relation between the coefficients of two cyclotomic polynomials whose indexes differ by a prime factor.
Cite
@article{arxiv.2508.02722,
title = {Divisibility criteria and coefficient formulas for cyclotomic polynomials},
author = {Laura De Carli and Maurizio Laporta},
journal= {arXiv preprint arXiv:2508.02722},
year = {2025}
}