We establish necessary and sufficient conditions for a polynomial to be divisible by a cyclotomic polynomial 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 propose a recursive relation between the coefficients of two cyclotomic polynomials whose indexes differ by a prime factor.
Divisibility criteria and coefficient formulas for cyclotomic polynomials / De Carli, L., Laporta, M.. - In: THE RAMANUJAN JOURNAL. - ISSN 1572-9303. - 70:44(2026), pp. 1-24. [10.1007/s11139-026-01421-6]
Divisibility criteria and coefficient formulas for cyclotomic polynomials
L. De Carli;M. Laporta
2026
Abstract
We establish necessary and sufficient conditions for a polynomial to be divisible by a cyclotomic polynomial 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 propose a recursive relation between the coefficients of two cyclotomic polynomials whose indexes differ by a prime factor.File in questo prodotto:
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