Gülsüm Yeliz Şentürk, Nurten Gürses and Salim Yüce

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 27, 2021, Number 4, Pages 219–235

DOI: 10.7546/nntdm.2021.27.4.219-235

**Full paper (PDF, 302 Kb)**

## Details

### Authors and affiliations

Gülsüm Yeliz Şentürk

*Faculty of Engineering and Architecture, Istanbul Gelisim University,
Department of Computer Engineering, 34310, Istanbul, Turkey*

Nurten Gürses

*Faculty of Arts and Sciences, Yildiz Technical University,
Department of Mathematics, 34220, Istanbul, Turkey*

Salim Yüce

*Faculty of Arts and Sciences, Yildiz Technical University,
Department of Mathematics, 34220, Istanbul, Turkey*

### Abstract

In this study, we have defined Fibonacci quaternion matrix and investigated its powers. We have also derived some important and useful identities such as Cassini’s identity using this new matrix.

### Keywords

- Horadam number
- Dual-generalized complex number
- Hyperbolic-generalized complex number
- Binet’s formula
- D’Ocagne’s identity
- Catalan’s identity
- Cassini’s identity

### 2020 Mathematics Subject Classification

- 11B37
- 11B39
- 11K31

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## Cite this paper

Şentürk, G. Y., Gürses, N., & Yüce, S. (2021). Fundamental properties of extended Horadam numbers. *Notes on Number Theory and Discrete Mathematics*, 27(4), 219-235, DOI: 10.7546/nntdm.2021.27.4.219-235.