Generalized Commutative Mersenne and Mersenne–Lucas Quaternion Polynomials

Dorota Bród; Anetta Szynal-Liana; Mirosław Liana

doi:10.2478/amsil-2025-0017

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Generalized Commutative Mersenne and Mersenne–Lucas Quaternion Polynomials

Annales Mathematicae Silesianae

Volume 40 (2026): Issue 1 (March 2026)

By: Dorota Bród , Anetta Szynal-Liana and Mirosław Liana

Open Access

|Nov 2025

Abstract

Generalized commutative quaternions generalize elliptic, parabolic and hyperbolic quaternions, bicomplex numbers, complex hyperbolic numbers and hyperbolic complex numbers. In this paper, we use the Mersenne numbers and polynomials in the theory of these quaternions. We introduce and study generalized commutative Mersenne quaternion polynomials and generalized commutative Mersenne–Lucas quaternion polynomials.

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Articles in this issue

DOI: https://doi.org/10.2478/amsil-2025-0017 | Journal eISSN: 2391-4238 | Journal ISSN: 0860-2107

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Language: English

Page range: 13 - 26

Submitted on: Jun 21, 2025

Accepted on: Oct 26, 2025

Published on: Nov 15, 2025

Published by: University of Silesia in Katowice, Institute of Mathematics

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

11B39,

11B37

Related subjects:

Mathematics,

General mathematics

© 2025 Dorota Bród, Anetta Szynal-Liana, Mirosław Liana, published by University of Silesia in Katowice, Institute of Mathematics
This work is licensed under the Creative Commons Attribution 4.0 License.

Volume 40 (2026): Issue 1 (March 2026)