Product Difference Fibonacci Identities Revisited: Quaternionic Generalizations of Everman and Koshy

Authors

  • Bahar Demirtürk Department of Fundamental Sciences, Faculty of Engineering and Architecture, 6 Izmir Bakır ̧cay University, Izmir, Turkiye
  • Nazim Topal Department of Fundamental Sciences, Faculty of Engineering and Architecture, 6 Izmir Bakır ̧cay University, Izmir, Turkiye

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i3.6492

Keywords:

generalized Fibonacci numbers, generalized Fibonacci quaternions, quaternions, product differences

Abstract

In this paper, we investigate new identities involving generalized Fibonacci and Lucas sequences, as well as their associated quaternions. After establishing the fundamental properties of these generalized number sequences, we derive quaternionic extensions of product-difference identities originally introduced by Everman and Koshy for Fibonacci numbers. These results not
only generalize classical identities, but also reveal new algebraic structures within the framework of generalized quaternion sequences.

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Published

2025-08-01

Issue

Vol. 18 No. 3: (July 2025)

Section

Number Theory

License

Copyright (c) 2025 Bahar Demirtürk, Nazim Topal

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How to Cite

Product Difference Fibonacci Identities Revisited: Quaternionic Generalizations of Everman and Koshy. (2025). European Journal of Pure and Applied Mathematics, 18(3). https://doi.org/10.29020/nybg.ejpam.v18i3.6492