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.