On Companion sequences associated with Leonardo quaternions: Applications over finite fields
Combinatorics
2025-01-22 v2
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.
Keywords
Cite
@article{arxiv.2403.01592,
title = {On Companion sequences associated with Leonardo quaternions: Applications over finite fields},
author = {Diana Savin and Elif Tan},
journal= {arXiv preprint arXiv:2403.01592},
year = {2025}
}