Results 1 to 10 of about 1,605,720 (180)

Towards a new generalized Simson’s identity [PDF]

Notes on Number Theory and Discrete Mathematics
This paper is an attempt to develop an elegant and simple generalization of what is usually called Simson’s Identity, with variations named after Cassini, Catalan and Gelin-Cesàro.
A. G. Shannon, H. M. Srivastava, József Sàndor   +2 more
doaj   +3 more sources

A bijective proof of Cassini's fibonacci identity

Discrete Mathematics, 1986
The authors provide a short combinatorial proof of the identity \(F^ 2_{n+1}-F_{n+2}F_ n=(-1)^{n+1}\), where \(F_ n\) denotes the n-th Fibonacci number.
M. Werman, Doron Zeilberger
exaly   +4 more sources

Split Quaternionic Representations of Horadam Sequences and Their Binet, Generating Function, and Cassini-Type Identities

Journal of Mathematics
This study establishes a novel algebraic connection between Horadam numbers and the split quaternion algebra. To this end, two fundamental constructs are introduced: the Fibonacci Sq,r-split quaternions and the Horadam sq,r-split quaternions, which ...
İskender Öztürk, Hasan Çakır
doaj   +3 more sources

Elliptic Solutions of Dynamical Lucas Sequences [PDF]

Entropy, 2021
We study two types of dynamical extensions of Lucas sequences and give elliptic solutions for them. The first type concerns a level-dependent (or discrete time-dependent) version involving commuting variables. We show that a nice solution for this system
Michael J. Schlosser, Meesue Yoo
doaj   +3 more sources

On Hybrid Numbers with Gaussian Leonardo Coefficients

Mathematics, 2023
We consider the Gaussian Leonardo numbers and investigate some of their amazing characteristic properties, including their generating function, the associated Binet formula and Cassini identity, and their matrix representation. Then, we define the hybrid
Nagihan Kara, Fatih Yilmaz
doaj   +3 more sources

On the connections between Fibonacci and Mulatu Numbers

Intermaths
In this work, we present a detailed study of the Fibonacci--Mulatu sequence, {FMn}, defined recursively by FMn+2=FMn+1+FMn with initial terms FM0 = 4 and FM1 = 1.
Eudes Antonio Costa, Élis Gardel da Costa Mesquita, Paula M. M. C. Catarino   +2 more
doaj   +4 more sources

Cassini, d'Ocagne, and Vajda identities for n-step Fibonacci numbers [PDF]

, 2022
Results of this paper concern $n$-determinants which we defined in the paper \cite{jan}. In the paper \cite{jabo}, $2$-determinants are considered. In this paper, we extend results from \cite{jabo} on $n$-determinants by proving that Cassini, d'Ocagne, Catalan and Vajda identities may be extended to hold for $n$-step Fibonacci numbers.
Milan Janjić
openaire   +3 more sources

Generalized Cassini identities via the generalized Fibonacci fundamental system. Applications

Indian Journal of Pure and Applied Mathematics, 2023
Based on the author's abstract: this paper explores the generalized Cassini identities for the weighted generalized Fibonacci sequences, through the associated generalized Fibonacci fundamental system. Some algebraic, combinatorics and analytic properties of these identities are established.
I. M. Craveiro, E. V. Pereira Spreafico, M. Rachidi   +2 more
openaire   +3 more sources

Fiboquadratic Sequences and Extensions of the Cassini Identity Raised From the Study of Rithmomachia [PDF]

, 2015
18 pages, 4 figures, 6 ...
Guardia, Tomás, Jiménez, Douglas
openaire   +3 more sources

The Quaterniontonic and Octoniontonic Fibonacci Cassini’s Identity: An Historical Investigation with the Maple’s Help [PDF]

International Electronic Journal of Mathematics Education, 2018
This paper discusses a proposal for exploration and verification of numerical and algebraic behavior correspondingly to Generalized Fibonacci model. Thus, it develops a special attention to the class of Fibonacci quaternions and Fibonacci octonions and with this assumption, the work indicates an investigative and epistemological route, with assistance ...
F. Alves
semanticscholar   +3 more sources