Results 21 to 30 of about 1,000 (210)

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
openaire   +2 more sources

Aplikasi Ring Kuadratik dalam Menyelesaikan Persamaan Pell [PDF]

, 2020
Artikel ini membahas tentang penerapan Metode ring  (kuadratik) dalam mencari solusi pada persamaan Pell. Persamaan Pell merupakan bagian dari persamaan Diophantine non linear yang penyelesaiannya berupa bilangan bulat dengan bentuk umum persamaannya ...
Abdy, Muhammad, Sanusi, Wahidah, Priono, Utami   +2 more
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The polynomial Pell equation

Elemente der Mathematik, 2004
The classic problem of Diophantine approximations consists in discovering good rational-\-numbered approximations of quadratic irrationalities of the form \(\sqrt d\), where \(d\) is a square-free natural number. This problem leads to the Pell equation \(x^2 - dy^2 = 1\) in whole integers \(x, y\). It turns out that you can acquire all solutions from a
Dubickas, Artūras, Steuding, Jörn
openaire   +2 more sources

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
doaj   +1 more source

Pell Equation - Theory and applications to cryptography [PDF]

, 2022
The Pell equation $x^2 − d y^2 = 1$ is a classical topic in number theory. There are well known methods for solving this equation, but there are still several important issues.
Simone Dutto
core  

On the negative Pell equation [PDF]

, 2019
Using a recent breakthrough of Smith, we improve the results of Fouvry and Kl\"uners on the solubility of the negative Pell equation. Let $\mathcal{D}$ denote the set of fundamental discriminants having no prime factors congruent to $3$ modulo $4 ...
Koymans, Peter, Milovic, Djordjo, Pagano, Carlo, Chan, Stephanie   +3 more
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A STUDY ON PELL EQUATION [PDF]

, 2020
Pell equation (alternatively called the Pell- Fermat equation) is a type of a Diophantine equation of the form 2 -Dye 2 =1 for a natural number D. If D is a perfect square, then pell equation can be rewritten as y).(x+√y) = 1.similarly, the trivial ...
R, RAMYA
core   +1 more source

Pell Collocation Method for Solving the Nonlinear Time–Fractional Partial Integro–Differential Equation with a Weakly Singular Kernel

Journal of Function Spaces, 2022
This article focuses on finding the numerical solution of the nonlinear time–fractional partial integro–differential equation. For this purpose, we use the operational matrices based on Pell polynomials to approximate fractional Caputo derivative ...
M. Taghipour, H. Aminikhah
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A numerical approach to solve hyperbolic telegraph equations via Pell–Lucas polynomials

Journal of Taibah University for Science, 2023
In this article, a collocation approximation is investigated for approximate solutions of hyperbolic telegraph partial differential equations (HTPDEs). The method is based on evenly spaced collocation points and Pell–Lucas polynomials (PLPs). The form of
Şuayip Yüzbaşı, Gamze Yıldırım
doaj   +1 more source