Results 61 to 70 of about 15,160 (203)
Identities relating six members of the Fibonacci family of sequences
Karpatsʹkì Matematičnì Publìkacìï, 2022 In this paper, we prove several identities each relating a sum of products of three terms coming from different members of the Fibonacci family of sequences with a comparable sum whose terms come from three other sequences.
R. Frontczak, T. Goy, M. Shattuck
doaj +1 more source
Gaussian Pell and Gaussian Pell-Lucas Quaternions
, 2021 The main aim of this work is to introduce the Gaussian Pell quaternion QGp(n) and Gaussian Pell-Lucas quaternion OGq(n), where the components of QGp(n) and QGq(n) are Pell numbers p(n) and Pell-Lucas numbers q(n), respectively.
ARSLAN, HASAN
core +1 more source
Diophantine equations on cross-multiplicative forms of the Pell and Pell-Lucas numbers
Balıkesir Üniversitesi Fen Bilimleri Enstitüsü DergisiThis study aims to explore all Pell numbers that are the product of two random Pell-Lucas numbers and all Pell-Lucas numbers that are the product of two random Pell numbers based on linear forms in logarithms of algebraic numbers using Matveev's theorem ...
Ahmet Emin, Ahmet Daşdemir
semanticscholar +1 more source
On Pell and Pell-Lucas Generalized Octonions
, 2021 In this study, we gave a generalization on Pell and Pell-Lucas octonions over the algebra $\mathbb{O}(a,b,c)$ where $a,b$ and $c$ are real numbers. For these number sequences, we obtain Binet formulas and gave some well-known identities such as Catalan's
Ümit TOKEŞER +7 more
core +2 more sources
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 +2 more
doaj +1 more source
On 3-parameter generalized quaternions with k-pell-lucas numbers as components
Journal of Physics: Conference SeriesAt present, numerous research studies have been conducted on Fibonacci quaternions and their generalizations. Recently, Şentürk and Ünal introduced 3-parameter generalized quaternions.
Deng Yong, Jian-Gang Tang
semanticscholar +1 more source
Diophantine tuples and product sets in shifted powers
Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.Abstract Let k⩾2$k\geqslant 2$ and n≠0$n\ne 0$. A Diophantine tuple with property Dk(n)$D_k(n)$ is a set of positive integers A$A$ such that ab+n$ab+n$ is a k$k$th power for all a,b∈A$a,b\in A$ with a≠b$a\ne b$. Such generalizations of classical Diophantine tuples have been studied extensively.
Ernie Croot, Chi Hoi Yip
wiley +1 more source
Mersenne-Horadam identities using generating functions
Karpatsʹkì Matematičnì Publìkacìï, 2020 The main object of the present paper is to reveal connections between Mersenne numbers $M_n=2^n-1$ and generalized Fibonacci (i.e., Horadam) numbers $w_n$ defined by a second order linear recurrence $w_n=pw_{n-1}+qw_{n-2}$, $n\geq 2$, with $w_0=a$ and ...
R. Frontczak, T.P. Goy
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Psychophysiology, Volume 63, Issue 2, February 2026.ABSTRACT Emotion is key to human communication, and inferring emotion in a speaker's voice is a cross‐cultural and cross‐linguistic capability. Electroencephalography (EEG) studies of neural mechanisms supporting emotion perception have reported that early components of the event‐related potential (ERP) are modulated by emotion.
Yichen Tang +2 more
wiley +1 more source
Three Drivers of 21st‐Century Changes in Ocean Tides
Journal of Geophysical Research: Oceans, Volume 131, Issue 1, January 2026.Abstract Numerical model simulations are conducted to study the response of barotropic ocean tides to 21st‐century climate change, as manifested by sea level rise, increasing ocean stratification, and expanding Antarctic ice shelf cavities. Emphasis is placed on surface elevations, with projections of M2 ${\mathrm{M}}_{2}$, S2 ${\mathrm{S}}_{2}$, K1 ${\
Lana Opel +8 more
wiley +1 more source