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arXiv · 2403.01592

On Companion sequences associated with Leonardo quaternions: Applications over finite fields

Diana Savin·Elif Tan
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Abstract

It is known that the quaternion algebras are central simple algebras and also clifford algebras. In this paper, we introduce a new class of quaternions called Lucas-Leonardo p-quaternions and derive several fundamental properties of these numbers. Furthermore, we investigate some applications related to companion sequences associated with Leonardo quaternions. In particular, we determine Lucas-Leonardo quaternions and Francois quaternions, which are zero divisors and invertible elements in the quaternion algebra over certain finite fields.

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Diana Savin, Elif Tan. 2025-01-18. On Companion sequences associated with Leonardo quaternions: Applications over finite fields. https://arxiv.org/abs/2403.01592

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