Generalization of an identity involving the generalized Fibonacci numbers and its applications.
Mohammad Farrokhi, D.G. (2009)
Integers
Similarity:
Mohammad Farrokhi, D.G. (2009)
Integers
Similarity:
Ahmet Daşdemir (2019)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
Similarity:
To date, many identities of different quaternions, including the Fibonacci and Lucas quaternions, have been investigated. In this study, we present Gelin-Cesáro identities for Fibonacci and Lucas quaternions. The identities are a worthy addition to the literature. Moreover, we give Catalan's identity for the Lucas quaternions.
Ekhad, Shalosh B., Mohammed, Mohamud (2003)
Integers
Similarity:
Carsten Elsner, Shun Shimomura, Iekata Shiokawa (2007)
Acta Arithmetica
Similarity:
Alexey Stakhov (2012)
Visual Mathematics
Similarity:
Grossman, George, Tefera, Akalu, Zeleke, Aklilu (2006)
International Journal of Mathematics and Mathematical Sciences
Similarity:
Edyta Hetmaniok, Bożena Piątek, Roman Wituła (2017)
Open Mathematics
Similarity:
The aim of the paper is to present the binomial transformation formulae of Fibonacci numbers scaled by complex multipliers. Many of these new and nontrivial relations follow from the fundamental properties of the so-called delta-Fibonacci numbers defined by Wituła and Słota. The paper contains some original relations connecting the values of delta-Fibonacci numbers with the respective values of Chebyshev polynomials of the first and second kind.
Chu, Wenchang, Di Claudio, Leontina Veliana (2003)
Integers
Similarity:
Čerin, Zvonko, Gianella, Gian Mario (2006)
Integers
Similarity:
Kılıç, Emrah, Ulutaş, Yücel Türker, Ömür, Neşe (2011)
Journal of Integer Sequences [electronic only]
Similarity:
Belbachir, Hacéne, Bouroubi, Sadek, Khelladi, Abdelkader (2008)
Annales Mathematicae et Informaticae
Similarity:
Vera W. de Spinadel (1999)
Visual Mathematics
Similarity:
Sprugnoli, Renzo (2006)
Integers
Similarity:
Horadam, A.F., Shannon, A.G. (1987)
Portugaliae mathematica
Similarity:
Diego Marques, Alain Togbé (2011)
Colloquium Mathematicae
Similarity:
In 2000, Florian Luca proved that F₁₀ = 55 and L₅ = 11 are the largest numbers with only one distinct digit in the Fibonacci and Lucas sequences, respectively. In this paper, we find terms of a linear recurrence sequence with only one block of digits in its expansion in base g ≥ 2. As an application, we generalize Luca's result by finding the Fibonacci and Lucas numbers with only one distinct block of digits of length up to 10 in its decimal expansion.