On bi-periodic Padovan and Perrin quaternions over finite fields
Abstract
In this paper, we investigate bi-periodic Padovan and bi-periodic Perrin quaternions in 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.
Fields of Study & Subjects
Advanced Mathematical Theories and Applications
Algebraic and Geometric Analysis
Rings
Modules
and Algebras
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 8 February 2026
- Language
- EN
- Document type
- Preprint