Results 1 to 10 of about 1,000 (210)

Pell Equations and ℱpl-Continued Fractions [PDF]

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   +2 more sources

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
doaj   +2 more sources

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

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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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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Polynomial Pell’s equation [PDF]

Proceedings of the American Mathematical Society, 2002
Consider the polynomial Pell’s equation X 2 −
Webb, William A., Yokota, Hisashi
openaire   +2 more sources