Pell–Padovan generalized quaternions

Zehra İşbilir and Nurten Gürses
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 27, 2021, Number 1, Pages 171–187
DOI: 10.7546/nntdm.2021.27.1.171-187
Full paper (PDF, 247 Kb)

Details

Authors and affiliations

Zehra İşbilir
Duzce University, Faculty of Arts and Sciences,
Department of Mathematics, 81620, Duzce, Turkey

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

Abstract

The aim of this article is to introduce Pell–Padovan generalized quaternions. It also derives new properties associated with these and takes into account negative indices. Additionally, it presents generating function, Binet-like formula, Simson formula, matrix representations, and several summation properties.

Keywords

• Pell–Padovan numbers
• Generalized quaternions
• Generating function
• Binet-like formula
• Simson formula

2010 Mathematics Subject Classification

• 11B37
• 11C20
• 11K31
• 11R52

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