Results 41 to 50 of about 1,051 (219)

Some Identities of Fibonacci and Lucas Quaternions by Quaternion Matrices

Düzce Üniversitesi Bilim ve Teknoloji Dergisi, 2019
In this paper, we consider one of the most knownFibonacci matrix Qand the Fibonacciquaternion matrix MQFn, where Qnis the n-th Fibonacci quaternion.In particular we define some new quaternion matrices.
Bahar Demirtürk Bitim
doaj   +1 more source

Reciprocal Formulae among Pell and Lucas Polynomials

Mathematics, 2022
Motivated by a problem proposed by Seiffert a quarter of century ago, we explicitly evaluate binomial sums with Pell and Lucas polynomials as weight functions.
Mei Bai, Wenchang Chu, Dongwei Guo
doaj   +1 more source

A Context-Free Grammar Associated with Fibonacci and Lucas Sequences

Journal of Mathematics, 2023
We introduce a context-free grammar G=s⟶s+d,d⟶s to generate Fibonacci and Lucas sequences. By applying the grammar G, we give a grammatical proof of the Binet formula.
Harold Ruilong Yang
doaj   +1 more source

On $k$-Fibonacci balancing and $k$-Fibonacci Lucas-balancing numbers

Karpatsʹkì Matematičnì Publìkacìï, 2021
The balancing number $n$ and the balancer $r$ are solution of the Diophantine equation $$1+2+\cdots+(n-1) = (n+1)+(n+2)+\cdots+(n+r). $$ It is well known that if $n$ is balancing number, then $8n^2 + 1$ is a perfect square and its positive square root is
S.E. Rihane
doaj   +1 more source

There are no multiply-perfect Fibonacci numbers

, 2011
Here, we show that no Fibonacci number (larger than 1) divides the sum of its ...
Lewis, Ryan H., Togbe, Alain, Kevin A. Broughan, Huguet, V. Janitzio Mejia, Marcos J. González, Broughan, Kevin A., Luca, Florian, V. Janitzio Mejía Huguet, Ryan H. Lewis, Alain Togbé, Gonzalez, Marcos J., Florian Luca   +11 more
core   +1 more source

Some new properties of hyperbolic k-Fibonacci and k-Lucas octonions [PDF]

Notes on Number Theory and Discrete Mathematics
The aim of this paper is to establish some novel identities for hyperbolic k-Fibonacci octonions and k-Lucas octonions. We prove these properties using the identities of k-Fibonacci and k-Lucas numbers, which we determined previously.
A. D. Godase
doaj   +1 more source

A new approach to Fibonacci Tessarines with Fibonacci and Lucas number components

Adıyaman University Journal of Science, 2021
In this paper, by using identities related to the tessarines, Fibonacci numbers and Lucas numbers we define Fibonacci tessarines and Lucas tessarines. We obtain Binet formulae, D’ocagnes identity and Cassini identity for these tessarines. We also give the identities of Fibonacci negatessarines and Lucas negatessarines and define new vector which are ...
BABADAĞ, Faik, USLU, Merve
openaire   +2 more sources

More identities on Fibonacci and Lucas hybrid numbers

, 2021
WOS:000665848000017We give several identities about Fibonacci and Lucas hybrid numbers. We introduce the Fibonacci and Lucas hybrid numbers with negative subscripts.
Yılmaz, Nazmiye
core   +1 more source

Mind the Gap: Linking Refactorings and Code Smells in Elixir

Journal of Software: Evolution and Process, Volume 38, Issue 5, May 2026.
ABSTRACT Elixir is a functional programming language increasingly used in the industry to develop scalable and fault‐tolerant concurrent systems more easily and with fewer computational resources. In previous studies, we cataloged 35 code smells and 82 refactorings tailored for this language, validating them with over 300 experienced developers ...
Lucas Vegi, Marco Túlio Valente
wiley   +1 more source

Fibonacci numbers and Lucas numbers

, 2016
Neste trabalho, exploramos os números de Fibonacci e de Lucas. A maioria dos resultados históricos sobre esses números são apresentados e provados. Ao longo do texto, um grande número de identidades a respeito dos números de Fibonacci e de Lucas são ...
Silva, Bruno Astrolino e
core   +1 more source