Results 51 to 60 of about 10,192,155 (339)

On Hybrid Hyper k-Pell, k-Pell–Lucas, and Modified k-Pell Numbers

Axioms, 2023
Many different number systems have been the topic of research. One of the recently studied number systems is that of hybrid numbers, which are generalizations of other number systems.
Elen Viviani Pereira Spreafico, Paula Catarino, Paulo Vasco   +2 more
doaj   +1 more source

Fibonacci–Lucas–Pell–Jacobsthal relations

Annales Mathematicae et Informaticae, 2022
In this paper, we prove several identities involving linear combinations of convolutions of the generalized Fibonacci and Lucas sequences. Our results apply more generally to broader classes of second-order linearly recurrent sequences with constant ...
R. Frontczak, T. Goy, M. Shattuck
semanticscholar   +1 more source

Series associated with harmonic numbers, Fibonacci numbers and central binomial coefficients $binom{2n}{n}$ [PDF]

Notes on Number Theory and Discrete Mathematics
We find various series that involve the central binomial coefficients $binom{2n}{n}$, harmonic numbers and Fibonacci numbers. Contrary to the traditional hypergeometric function _pF_q approach, our method utilizes a straightforward transformation to ...
Segun Olofin Akerele, Olamide Esther Salami   +1 more
doaj   +1 more source

Lucas non-Wieferich primes in arithmetic progressions and the abc conjecture

Open Mathematics, 2023
We prove the lower bound for the number of Lucas non-Wieferich primes in arithmetic progressions. More precisely, for any given integer k≥2k\ge 2, there are ≫logx\gg \hspace{0.25em}\log x Lucas non-Wieferich primes p≤xp\le x such that p≡±1(modk)p\equiv ...
Anitha K., Fathima I. Mumtaj, Vijayalakshmi A. R.   +2 more
doaj   +1 more source

Incomplete Bivariate Fibonacci and Lucas 𝑝-Polynomials

Discrete Dynamics in Nature and Society, 2012
We define the incomplete bivariate Fibonacci and Lucas 𝑝-polynomials. In the case 𝑥=1, 𝑦=1, we obtain the incomplete Fibonacci and Lucas 𝑝-numbers. If 𝑥=2, 𝑦=1, we have the incomplete Pell and Pell-Lucas 𝑝-numbers.
Dursun Tasci, Mirac Cetin Firengiz, Naim Tuglu   +2 more
doaj   +1 more source

Modified Lucas-Washburn theory for fluid filling in nanotubes.

Physical Review E, 2022
Ultrafast water transport in carbon nanotubes (CNTs) has drawn a great deal of attention in a number of applications, such as water desalination, power generation, and biomolecule detection.
M. Heiranian, N. Aluru
semanticscholar   +1 more source

On some series involving the binomial coefficients $binom{3n}{n}$ [PDF]

Notes on Number Theory and Discrete Mathematics
Using a simple transformation, we obtain much simpler forms for some series involving binomial coefficients $binom{3n}{n}$ derived by Necdet Batir. New evaluations are given and connections with Fibonacci numbers and the golden ratio are established ...
Kunle Adegoke, Robert Frontczak, Taras Goy   +2 more
doaj   +1 more source

A TILING INTERPRETATION FOR (p,q)-FIBONACCI AND (p,q)-LUCAS NUMBERS

Journal of Universal Mathematics, 2022
In this paper, we introduce a tiling approach to (p,q)-Fibonacci and (p,q)-Lucas numbers that generalize of the well-known Fibonacci, Lucas, Pell, Pell-Lucas, Jacobsthal ve Jacobsthal-Lucas numbers.
Yasemin Taşyurdu, Naime Şeyda Türkoğlu   +1 more
semanticscholar   +1 more source

Linear forms in Lucas numbers

Indagationes Mathematicae, 1993
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +2 more sources

LUCAS NUMBERS TRIANGLE

, 2021
{"references": ["1.\tR. Sivaraman, Number Triangles and Metallic Ratios, International Journal of Engineering and Computer Science, Volume 10, Issue 8, pp. 25365 \u2013 25369. 2.\tR. Sivaraman, Generalized Pascal's Triangle and Metallic Ratios, International Journal of Research, Volume 9, Issue 7, pp. 179 \u2013 184. 3.\tR.
openaire   +1 more source