Results 1 to 10 of about 20,503 (203)

Dirichlet and Neumann Problems for String Equation, Poncelet Problem and Pell-Abel Equation [PDF]

Symmetry, Integrability and Geometry: Methods and Applications, 2006
We consider conditions for uniqueness of the solution of the Dirichlet or the Neumann problem for 2-dimensional wave equation inside of bi-quadratic algebraic curve.
Vladimir P. Burskii, Alexei S. Zhedanov
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Solutions of equations x2−(p2q2±3p)y2=±kt

Examples and Counterexamples, 2022
In the present paper, we have solved the equation x2−(p2q2±3p)y2=kt,x2−(p2q2±5p)y2=ktand expressed its positive integer solutions in terms of generalized Fibonacci, generalized Lucas and generalized Pell, generalized Pell–Lucas sequences.
Roji Bala, Vinod Mishra
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On perfect powers in $k$-generalized Pell sequence [PDF]

Mathematica Bohemica, 2023
Let $k\geq2$ and let $(P_n^{(k)})_{n\geq2-k}$ be the $k$-generalized Pell sequence defined by \begin{equation*} P_n^{(k)}=2P_{n-1}^{(k)}+P_{n-2}^{(k)}+\cdots+P_{n-k}^{(k)} \end{equation*}for $n\geq2$ with initial conditions \begin{equation*} P_{-(k-2)}^{(
Zafer Şiar, Refik Keskin, Elif Segah Öztaş   +2 more
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The Polynomial Solutions of Quadratic Diophantine Equation X2−ptY2+2KtX+2ptLtY = 0

Journal of Mathematics, 2021
In this study, we consider the number of polynomial solutions of the Pell equation x2−pty2=2 is formulated for a nonsquare polynomial pt using the polynomial solutions of the Pell equation x2−pty2=1.
Hasan Sankari, Ahmad Abdo
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Pell’s Equation [PDF]

Formalized Mathematics, 2017
SummaryIn this article we formalize several basic theorems that correspond to Pell’s equation. We focus on two aspects: that the Pell’s equationx2−Dy2= 1 has infinitely many solutions in positive integers for a givenDnot being a perfect square, and that based on the least fundamental solution of the equation when we can simply calculate algebraically ...
Acewicz, Marcin, Pąk, Karol
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Pell Equations and ℱpl-Continued Fractions

Journal of Mathematics, 2022
In this note, the solvability of the Pell equation, X2−DY2=1, is discussed over ℤ×plℤ. In particular, we show that this equation is solvable over ℤ×plℤ for each prime p and natural number l.
Seema Kushwaha
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Polynomial Pell’s equation [PDF]

Proceedings of the American Mathematical Society, 2002
Summary: Consider the polynomial Pell equation \(X^2 -DY^2 = 1\), where \(D = A^2 + 2C\) is a monic polynomial in \({\mathbb Z}[x]\) and \(\deg{C} < \deg{A}\). Then for \(A, C \in{\mathbb Q}[x]\), \(\deg{C} < 2\), and \(B = A/C \in{\mathbb Q}[x]\), necessary and sufficient condition for the polynomial Pell equation to have a nontrivial solution in ...
Webb, William A., Yokota, Hisashi
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Équation de Pell–Abel et applications

Comptes Rendus. Mathématique, 2022
In this paper, we show that there are solutions of degree $r$ of the equation of Pell–Abel on some real hyperelliptic curve of genus $g$ if and only if $ r > g$.
Gendron, Quentin
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Pell Collocation Pseudo Spectral Scheme for One-Dimensional Time-Fractional Convection Equation with Error Analysis

Journal of Function Spaces, 2022
In the current manuscript, we implement the collocation method to obtain an approximate solution of one-dimensional time-fractional convection equation. The operational matrices of Pell polynomials are applied to solve the fractional partial differential
A. S. Mohamed
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Security Issues of Novel RSA Variant

IEEE Access, 2022
The RSA is one of the current default cryptosystems that provides security with applications such as encryptions and digital signatures. It is important to further study the weak characteristics of the RSA to ensure correct utilisation in order not to be
Abderrahmane Nitaj, Muhammad Rezal Bin Kamel Ariffin, Nurul Nur Hanisah Adenan, Terry Shue Chien Lau, Jiahui Chen   +4 more
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