Bivariate Mersenne polynomials and matrices

Francisco Regis Vieira Alves
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 26, 2020, Number 3, Pages 83–95
DOI: 10.7546/nntdm.2020.26.3.83-95
Full paper (PDF, 254 Kb)

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Authors and affiliations

Francisco Regis Vieira Alves
Department of Mathematics, Institute Federal of Tecnology of State of Ceara (IFCE)
Fortaleza-CE, Brazil

Abstract

In this work we present a new notion called bivariate polynomials of Mersenne. We will also discuss certain related matrix properties. Finally, we introduce a notion of the bivariate quaternions of Mersenne.

Keywords

• Mersenne sequence
• Matrix properties
• Bivariate Mersenne sequence

2010 Mathematics Subject Classification

• 11B37
• 11B39

References

1. Catarino, P. M. M. C., Campos, H., & Vasco, P. (2016). On the Mersenne sequence, Annales Mathematicae et Informaticae, 1(46), 36–53.
2. Catalani, M. (2002). Generalized Bivariate Fibonacci Polynomials, Arxiv, 1–11.
3. Dasdemir, A., & Bilgici, G. (2019). Gaussian Mersenne numbers and generalized Mersenne quaternions, Notes on Number Theory and Discrete Mathematics, 25(3), 87–96.