Results 31 to 40 of about 20,503 (203)
On $k$-Pell numbers which are sum of two Narayana's cows numbers [PDF]
Mathematica BohemicaFor any positive integer $k\geq2$, let $(P_n^{(k)})_{n\geq2-k}$ be the $k$-generalized Pell sequence which starts with $0,\cdots,0,1$ ($k$ terms) with the linear recurrence P_n^{(k)} = 2P_{n-1}^{(k)}+P_{n-2}^{(k)}+\cdots+P_{n-k}^{(k)}\quad\text{for} n\
Kouèssi Norbert Adédji +2 more
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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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On the intersections of Fibonacci, Pell, and Lucas numbers [PDF]
, 2010 We describe how to compute the intersection of two Lucas sequences of the forms $\{U_n(P,\pm 1) \}_{n=0}^{\infty}$ or $\{V_n(P,\pm 1) \}_{n=0}^{\infty}$ with $P\in\mathbb{Z}$ that includes sequences of Fibonacci, Pell, Lucas, and Lucas-Pell numbers.
Bilu +13 more
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A Family of the Zeckendorf Theorem Related Identities [PDF]
, 2015 In this paper we present a family of identities for recursive sequences arising from a second order recurrence relation, that gives instances of Zeckendorf representation.
Martinjak, Ivica
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Solution of certain Pell equations [PDF]
Asian-European Journal of Mathematics, 2018 Let [Formula: see text] be any positive integers such that [Formula: see text] and [Formula: see text] is a square free positive integer of the form [Formula: see text] where [Formula: see text] and [Formula: see text] The main focus of this paper is to find the fundamental solution of the equation [Formula: see text] with the help of the continued ...
Zahid Raza, Hafsa Masood Malik
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The cubic Pell equation $L$-function
Acta Arithmetica, 2023 For $d > 1$ a cubefree rational integer, we define an $L$-function (denoted $L_d(s)$) whose coefficients are derived from the cubic theta function for $\mathbb Q\left(\sqrt{-3}\right)$. The Dirichlet series defining $L_d(s)$ converges for $\text{Re}(s) > 1$, and its coefficients vanish except at values corresponding to integral solutions of $mx^3
Goldfeld, Dorian, Hinkle, Gerhardt
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Three Diophantine equations concerning the polygonal numbers [PDF]
Notes on Number Theory and Discrete MathematicsMany authors investigated the problem about the linear combination of two polygonal numbers being a perfect square, i.e., the Diophantine equation mPₖ(x)+nPₖ(y)=z², where Pₖ(x) denotes the x-th k-polygonal number and m, n are positive integers.
Yong Zhang, Mei Jiang, Qiongzhi Tang
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Applications of some special numbers obtained from a difference equation of degree three
, 2017 In this paper we present applications of some special numbers obtained from a difference equation of degree three, especially in the Coding Theory. As a particular case, we obtain the generalized Pell-Fibonacci-Lucas numbers, which were extended to the ...
Flaut, Cristina, Savin, Diana
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On the sequences of $(q,k)$-generalized Fibonacci numbers [PDF]
Mathematica BohemicaWe consider a new family of recurrence sequences, the $(q,k)$-generalized Fibonacci numbers. These sequences naturally extend the well-known sequences of $k$-generalized Fibonacci numbers and generalized $k$-order Pell numbers.
Jean Lelis +3 more
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MathematicsThis paper introduces a collocation algorithm for numerically solving the third-order Gilson–Pickering equation (GPE) and the classical Rosenau–Hyman equation (RHE). We employ newly developed shifted Pell polynomials as basis functions.
Mohamed A. Abdelkawy +4 more
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