Results 21 to 30 of about 21,203 (185)
Pell and Pell-Lucas numbers of the form $-2^a-3^b+5^c$ [PDF]
, 2020 summary:In this paper, we find all Pell and Pell-Lucas numbers written in the form $-2^a-3^b+5^c$, in nonnegative integers $a$, $b$, $c$, with $0\leq \max \{a,b\}\leq c$
Qu, Yunyun, Zeng, Jiwen
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A New Generalization of Pell-Lucas Numbers (Bi-Periodic Pell-Lucas Sequence)
Communications in Mathematics and Applications, 2019 In this study, we bring into light, a new generalization of the Jacobsthal Lucas numbers, which shall also be called the bi-periodic Jacobsthal Lucas sequence as \begin{align*} Q_{n}= \begin{cases} 2bQ_{n-1}+Q_{n-2},&\text{if} \ n \ \text{is even} \\ 2aQ_{n-1}+Q_{n-2},&\text{if} \ n \ \text{is odd}% \end{cases} \text{\ \ }n\geq 2, \end{align*} with ...
Sukran Uygun, Hasan Karatas
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Properties of hyperbolic generalized Pell numbers [PDF]
, 2020 In this paper, we introduce the generalized hyperbolic Pell numbers over the bidimensional Clifford algebra of hyperbolic numbers. As special cases, we deal with hyperbolic Pell and hyperbolic Pell–Lucas numbers.
Yüksel Soykan, Melih Göcen
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Abstract and Applied Analysis, 2014 Circulant matrices may play a crucial role in solving various differential equations. In this paper, the techniques used herein are based on the inverse factorization of polynomial.
Tingting Xu, Zhaolin Jiang, Ziwu Jiang
doaj +1 more source
Primality tests, linear recurrent sequences and the Pell equation [PDF]
, 2022 We study new primality tests based on linear recurrent sequences of degree two exploiting a matrix approach. The classical Lucas test arises as a particular case and we see how it can be easily improved.
Di Scala, Antonio +7 more
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Fibonacci-Like sequence associated with k-Pell, k-Pell-Lucas and Modified k-Pell sequences [PDF]
, 2017 Fibonacci sequence is a well known example of second order linear recurrence relatio. Besides Fibonacci numbers and their generalizations have many applications as well as interesting properties almost in every field of science such as in Physics ...
Wani, A. A. +5 more
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Diophantine equations for additive Pell numbers in Pell, Pell–Lucas, and Modified Pell numbers [PDF]
Notes on Number Theory and Discrete MathematicsThis paper investigates the Diophantine equations arising from ternary additive problems of Pell, Pell-Lucas, and Modified Pell numbers. Specifically, we characterize all integer solutions to the equation Pₙ+Pₘ+Pᵣ=Xₖ, X∈{P,Q,R}, where Pᵢ, Qᵢ, and Rᵢ ...
Ahmet Emin, Ahmet Daşdemir
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The Third Order Jacobsthal Octonions: Some Combinatorial Properties
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2018 Various families of octonion number sequences (such as Fibonacci octonion, Pell octonion and Jacobsthal octonion) have been established by a number of authors in many di erent ways.
Cerda-Morales Gamaliel
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Non-Fisherian generalized Fibonacci numbers [PDF]
Notes on Number Theory and Discrete MathematicsUsing biology as inspiration, this paper explores a generalization of the Fibonacci sequence that involves gender biased sexual reproduction. The female, male, and total population numbers along with their associated recurrence relations are considered ...
Thor Martinsen
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Multiplicatively dependent integer vectors on a hyperplane
Journal of the London Mathematical Society, Volume 114, Issue 1, July 2026.Abstract We establish several asymptotic formulae and upper bounds for the count of multiplicatively dependent integer vectors that lie on a fixed affine hyperplane and have bounded height. This work constitutes a direct extension of the results obtained by Pappalardi, Sha, Shparlinski, and Stewart.
Muhammad Afifurrahman +2 more
wiley +1 more source