An inequality for Fibonacci numbers
Horst Alzer, Florian Luca (2022)
Mathematica Bohemica
Similarity:
We extend an inequality for Fibonacci numbers published by P. G. Popescu and J. L. Díaz-Barrero in 2006.
Horst Alzer, Florian Luca (2022)
Mathematica Bohemica
Similarity:
We extend an inequality for Fibonacci numbers published by P. G. Popescu and J. L. Díaz-Barrero in 2006.
Alexey Stakhov (2012)
Visual Mathematics
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.
Czesław Stępniak (2014)
Discussiones Mathematicae Probability and Statistics
Similarity:
Recent model of lifetime after a heart attack involves some integer coefficients. Our goal is to get these coefficients in simple way and transparent form. To this aim we construct a schema according to a rule which combines the ideas used in the Pascal triangle and the generalized Fibonacci and Lucas numbers
Alpert, Hannah (2009)
Integers
Similarity:
Dmitriy Weise (1999)
Visual Mathematics
Similarity:
Mohammad Farrokhi, D.G. (2009)
Integers
Similarity:
Alexey Stakhov (2009)
Visual Mathematics
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.
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.
Emerson, Nathaniel D. (2006)
Journal of Integer Sequences [electronic only]
Similarity:
Cigler, Johann (2003)
Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only]
Similarity:
Kiliç, Emrah, Tan, Elif (2010)
Integers
Similarity:
Vera W. de Spinadel (1999)
Visual Mathematics
Similarity:
Christian Ballot, Florian Luca (2007)
Acta Arithmetica
Similarity: