Results 21 to 30 of about 20,503 (203)
Diophantine equations for additive Pell numbers in Pell, Pell–Lucas, and Modified Pell numbers [PDF]
Notes on Number Theory and Discrete MathematicsThis 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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Simultaneous Pell equations [PDF]
AIP Conference Proceedings, 2016 This paper will discuss the solutions on the simultaneous Pell equations x2 − my2 = 1 and y2 − 11z2 = 1 where m is square free. By looking at the pattern of the solutions, some theorems will be developed. The solutions to these simultaneous equations are (x, y, z, m) = (50i − 1, 10, 3, mi) and (50i + 1, 10, 3, mi) for some expressions of mi where i is ...
N. A. Sihabudin +2 more
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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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Smooth values of some quadratic polynomials [PDF]
, 2010 In this paper, using a method of Luca and the author, we find all values $x$ such that the quadratic polynomials $x^2+1,$ $x^2+4,$ $x^2+2$ and $x^2-2$ are 200-smooth and all values $x$ such that the quadratic polynomial $x^2-4$ is 100-smooth.Comment: 12 ...
Buchmann +6 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 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
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Explicit algebraic solution of Zolotarev's First Problem for low-degree polynomials
Journal of Numerical Analysis and Approximation Theory, 2019 E.I. Zolotarev's classical so-called First Problem (ZFP), which was posed to him by P.L. Chebyshev, is to determine, for a given \(n\in{\mathbb N}\backslash\{1\}\) and for a given \(s\in{\mathbb R}\backslash\{0\}\), the monic polynomial solution \(Z ...
Heinz Joachim Rack, Robert Vajda
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On the double EPW sextic associated to a Gushel-Mukai fourfold [PDF]
, 2018 In analogy to the case of cubic fourfolds, we discuss the conditions under which the double cover $\tilde{Y}_A$ of the EPW sextic hypersurface associated to a Gushel-Mukai fourfold is birationally equivalent to a moduli space of (twisted) stable sheaves ...
Pertusi, Laura
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Balances in the Set of Arithmetic Progressions
Axioms, 2021 This article focuses on searching and classifying balancing numbers in a set of arithmetic progressions. The sufficient and necessary conditions for the existence of balancing numbers are presented.
Chan-Liang Chung +2 more
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Two divisors of (n^2+1)/2 summing up to {\delta}n+{\epsilon}, for {\delta} and {\epsilon} even [PDF]
, 2014 In this paper we are dealing with the problem of the existence of two divisors of $(n^2+1)/2$ whose sum is equal to $\delta n+\varepsilon$, in the case when $\delta$ and $\varepsilon$ are even, or more precisely in the case in which $\delta\equiv ...
Bujačić, Sanda
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