Results 51 to 60 of about 613 (205)

On a Linear Diophantine Problem Involving the Fibonacci and Lucas Sequences

Integers, 2015
See the abstract in the attached pdf.
Sanjit Singh Batra, Nikhil Kumar 0001, Amitabha Tripathi   +2 more
openaire   +4 more sources

On Generalized Lucas Pseudoprimality of Level k

Mathematics, 2021
We investigate the Fibonacci pseudoprimes of level k, and we disprove a statement concerning the relationship between the sets of different levels, and also discuss a counterpart of this result for the Lucas pseudoprimes of level k.
Dorin Andrica, Ovidiu Bagdasar
doaj   +1 more source

Divisibility Properties of the Fibonacci, Lucas, and Related Sequences [PDF]

ISRN Algebra, 2014
We use matrix techniques to give simple proofs of known divisibility properties of the Fibonacci, Lucas, generalized Lucas, and Gaussian Fibonacci numbers. Our derivations use the fact that products of diagonal matrices are diagonal together with Bezout’s identity.
Thomas Jeffery, Rajesh Pereira
openaire   +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

A Matrix Approach for Divisibility Properties of the Generalized Fibonacci Sequence

Discrete Dynamics in Nature and Society, 2013
We give divisibility properties of the generalized Fibonacci sequence by matrix methods. We also present new recursive identities for the generalized Fibonacci and Lucas sequences.
Aynur Yalçiner
doaj   +1 more source

Derivative Sequences of Fibonacci and Lucas Polynomials [PDF]

, 1991
Let us consider the Fibonacci polynomials U n(x) and the Lucas polynomials V n (x) (or simply U n and Vn, if there is no danger of confusion) defined as $$ {U_n} = x{U_{n - 1}} + {U_{n - 2}}({U_0} = 0,{U_1} = 1) $$ (1.1) and $$ {V_n} = x{V_{n - 2}}({V_0} = 2,V = x) $$ (1.2) where x is an indeterminate.
Piero Filipponi, Alwyn F. Horadam
openaire   +1 more source

Exploring Generalized $2^k$-Fibonacci Sequence: A New Family of the Fibonacci Sequence

Communications in Advanced Mathematical Sciences
The focus of this paper is to study the $2^k$–Fibonacci sequence, which is defined for all integers $2^k$, and its connections with both the Fibonacci and the Fibonacci-Lucas sequences.
Elis Gardel Costa Mesquista, Eudes Antonio Costa, Paula Maria Machado Cruz Catarino   +2 more
doaj   +1 more source

On sums of k-generalized Fibonacci and k-generalized Lucas numbers as first and second kinds of Thabit numbers [PDF]

Notes on Number Theory and Discrete Mathematics
Let (Fᵣ⁽ᵏ⁾)ᵣ≥2-k and (Lᵣ⁽ᵏ⁾)ᵣ≥2-k be generalizations of the Fibonacci and Lucas sequences, where k≥2. For these sequences the initial k terms are 0,0,...,0, 1 and 0,0,...,2,1, and each subsequent term is the sum of the preceding k terms.
Hunar Sherzad Taher, Saroj Kumar Dash
doaj   +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

Copper ratio obtained by generalizing the Fibonacci sequence

AIP Advances
In this study, we define a new generalization of the Fibonacci sequence that gives the copper ratio, and we will call it the copper Fibonacci sequence. In addition, inspired by the copper Fibonacci definition, we also define copper Lucas sequences, and ...
Engin Özkan, Hakan Akkuş
doaj   +1 more source