Results 11 to 20 of about 20,503 (203)

Pell-Lucas polynomials for numerical treatment of the nonlinear fractional-order Duffing equation

Demonstratio Mathematica, 2023
The nonlinear fractional-order cubic-quintic-heptic Duffing problem will be solved through a new numerical approximation technique. The suggested method is based on the Pell-Lucas polynomials’ operational matrix in the fractional and integer orders.
El-Sayed Adel Abd Elaziz
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Polynomial Pell's equation–II

Journal of Number Theory, 2004
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Webb, W.A., Yokota, H.
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Fermat and Mersenne numbers in $k$-Pell sequence

Математичні Студії, 2021
For an integer $k\geq 2$, let $(P_n^{(k)})_{n\geq 2-k}$ be the $k$-generalized Pell sequence, which starts with $0,\ldots,0,1$ ($k$ terms) and each term afterwards is defined by the recurrence $ P_n^{(k)}=2P_{n-1}^{(k)}+P_{n-2}^{(k)}+\cdots +P_{n-k}^{(k)}
B. Normenyo, S. Rihane, A. Togbe
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Lucas sequences and repdigits [PDF]

Mathematica Bohemica, 2022
Let $(G_n)_{n \geq1}$ be a binary linear recurrence sequence that is represented by the Lucas sequences of the first and second kind, which are $\{U_n\}$ and $\{V_n\}$, respectively.
Hayder Raheem Hashim, Szabolcs Tengely
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On some new results for the generalised Lucas sequences

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2021
In this paper we introduce the functions which count the number of generalized Lucas and Pell-Lucas sequence terms not exceeding a given value x and, under certain conditions, we derive exact formulae (Theorems 3 and 4) and establish asymptotic limits ...
Andrica Dorin, Bagdasar Ovidiu, Ţurcaş George Cătălin   +2 more
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Simultaneous Pell Equations

Journal of Number Theory, 1996
It is known that for each pair of non-zero integers, the number \(N(a,b)\) of triples of positive integers \(x,y,z\) satisfying the two Pell equations \[ x^2-az^2=1,\qquad y^2-bz^2=1\tag{1} \] is finite. In fact, this follows from Siegel's theorem that there are only finitely many integral points on a curve of genus 1.
Rickert, John, Masser, D.W.
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Algebraic Coding Theory Using Pell Equation x2 − 8y2 = 1

Ratio Mathematica, 2023
An interdisciplinary field with significant practical use is cryptography. The difficulty of specific mathematical computing tasks affects a public key cryptosystem’s security. The technique for coding and decoding the messages was described in this work,
Janaki G, Gowri Shankari A
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Some Criteria for Class Numbers to Be Non-One

Journal of Mathematics, 2020
Let d be a positive integer which is not a perfect square and n be any nonzero fixed integer. Then, the equation x2−dy2=n is known as the general Pell equation. In this paper, we give some criteria for class numbers of certain real quadratic fields to be
Ahmad Issa, Hasan Sankari
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Polynomial Pell's Equations [PDF]

Proceedings of the American Mathematical Society, 1976
The polynomial Pell’s equation is P 2 − ( x 2 + d ) Q 2 = 1 {P^2} - ({x^2} + d){Q^2} = 1 , where d d is an integer ...
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Pell–Lucas collocation method for numerical solutions of two population models and residual correction

Journal of Taibah University for Science, 2020
Our aim in this article is to present a collocation method to solve two population models for single and interacting species. For this, logistic growth model and prey–predator model are examined.
Şuayip Yüzbaşı, Gamze Yıldırım
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