COMBINATORIAL PROOFS OF SOME IDENTITIES INVOLVING FIBONACCI AND LUCAS NUMBERS
By
M. Tamba¹ and Y. S. Valaulikar²
¹School of Physical and Applied Sciences
²Ex- Faculty Goa University, Taleigaon Plateau, Goa, India-403206
Email : tamba@unigoa.ac.in, ysv@unigoa.ac.in ; valaulikarys@gmail.com
(Received: February 21, 2023; In format: March 02, 2023; Accepted: April 02, 2023)
DOI: https://doi.org/10.58250/jnanabha.2023.53123
Abstract
Using combinatorial methods, we obtain some identities, involving binomial coefficients, for Fibonacci and Lucas numbers. We define a set and show that the cardinality of this set equals Fibonacci number. We discuss some properties of this set. Technique has been extended to obtain results for Lucas numbers.
2020 Mathematical Sciences Classification: 11B39, 11B65, 11B75
Keywords and Phrases: Fibonacci numbers; Lucas numbers; Binomial coefficients; Cardinality of a set