Fibonacci and Lucas Numbers and their    
Bi-Complex Extension

Molhu Prasad Jaiswal; Narayan Prasad Pahari; Purushottam Parajuli; Nabaraj Adhikari

doi:https://doi.org/10.14445/22315373/IJMTT-V71I9P102

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 71 | Issue 9 | Year 2025 | Article Id. IJMTT-V71I9P102 | DOI : https://doi.org/10.14445/22315373/IJMTT-V71I9P102

Fibonacci and Lucas Numbers and their Bi-Complex Extension

Molhu Prasad Jaiswal, Narayan Prasad Pahari, Purushottam Parajuli, Nabaraj Adhikari

Received	Revised	Accepted	Published
13 Jul 2025	15 Aug 2025	03 Sep 2025	18 Sep 2025

Citation :

Molhu Prasad Jaiswal, Narayan Prasad Pahari, Purushottam Parajuli, Nabaraj Adhikari, "Fibonacci and Lucas Numbers and their Bi-Complex Extension," International Journal of Mathematics Trends and Technology (IJMTT), vol. 71, no. 9, pp. 9-16, 2025. Crossref, https://doi.org/10.14445/22315373/IJMTT-V71I9P102

Abstract

This paper aims to introduce a new type of Lucas and Fibonacci numbers, which are said to be bi-complex Lucas and bi-complex Fibonacci numbers. Also, we prove the D’ocagne identity. Further, we give the relation between the identities of negabicomplex Lucas numbers, negabicomplex Fibonacci numbers, and the Binet formula.

Keywords

Bi-complex numbers, Binet formula, Fibonacci numbers, Lucas numbers.

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