On bi-periodic Padovan and Perrin quaternions over finite fields
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866908820181090304 |
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| author | Savin, Diana Tan, Elif |
| author_facet | Savin, Diana Tan, Elif |
| contents | In this paper, we investigate bi-periodic Padovan and bi-periodic Perrin quaternions over the quaternion algebra Q_Zp. We introduce the bi-periodic Perrin sequence and clarify its structural relationship with the bi-periodic Padovan sequence. By extending these sequences to the quaternion setting, we analyze their norm properties in the modular framework. For suitable choices of twin prime coefficients, we derive explicit criteria characterizing zero divisors and invertible elements in Q_Zp. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_07894 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On bi-periodic Padovan and Perrin quaternions over finite fields Savin, Diana Tan, Elif Number Theory Combinatorics Rings and Algebras 11A07, 11B37, 11B39, 11R52, 16G30 In this paper, we investigate bi-periodic Padovan and bi-periodic Perrin quaternions over the quaternion algebra Q_Zp. We introduce the bi-periodic Perrin sequence and clarify its structural relationship with the bi-periodic Padovan sequence. By extending these sequences to the quaternion setting, we analyze their norm properties in the modular framework. For suitable choices of twin prime coefficients, we derive explicit criteria characterizing zero divisors and invertible elements in Q_Zp. |
| title | On bi-periodic Padovan and Perrin quaternions over finite fields |
| topic | Number Theory Combinatorics Rings and Algebras 11A07, 11B37, 11B39, 11R52, 16G30 |
| url | https://arxiv.org/abs/2602.07894 |