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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
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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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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
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Markov Triples with Generalized Pell Numbers
Mathematics, 2023 For an integer k≥2, let (Pn(k))n be the k-generalized Pell sequence which starts with 0,…,0,1 (k terms), and each term afterwards is given by Pn(k)=2Pn−1(k)+Pn−2(k)+⋯+Pn−k(k). In this paper, we determine all solutions of the Markov equation x2+y2+z2=3xyz,
Julieth F. Ruiz +2 more
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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
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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 +3 more
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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 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
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