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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2508.02722 |
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| _version_ | 1866918114172600320 |
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| author | De Carli, Laura Laporta, Maurizio |
| author_facet | De Carli, Laura Laporta, Maurizio |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_02722 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Divisibility criteria and coefficient formulas for cyclotomic polynomials De Carli, Laura Laporta, Maurizio Number Theory 12D10 05E05 11C08 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. |
| title | Divisibility criteria and coefficient formulas for cyclotomic polynomials |
| topic | Number Theory 12D10 05E05 11C08 |
| url | https://arxiv.org/abs/2508.02722 |