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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 Mathematics
This 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
doaj   +2 more sources

Polynomial Pell's Equation–II

Journal of Number Theory, 2004
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Webb, W.A., Yokota, H.
exaly   +3 more sources

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
doaj   +1 more source

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
doaj   +1 more source

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
doaj   +1 more source

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 ...
Marcin Acewicz, Karol Pak
openaire   +2 more sources

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
doaj   +1 more source

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
doaj   +1 more source

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
doaj   +1 more source

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
doaj   +1 more source