Results 21 to 30 of about 623 (119)
ON GENERALIZED (k, r) – GAUSS PELL NUMBERS
Journal of Science and Arts, 2021 We define the generalized (k, r) – Gauss Pell numbers by using the definition of a distance between numbers. Then we examine their properties and give some important identities for these numbers. In addition, we present the generating functions for these numbers and the sum of the terms of the generalized (k,r)- Gauss Pell numbers.
BAHAR KULOĞLU, ENGİN ÖZKAN
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Matrix Manipulations for Properties of Pell p -Numbers and their Generalizations [PDF]
Analele Universitatii "Ovidius" Constanta - Seria Matematica, 2020 Abstract In this paper, we define the Pell-Pell p -sequence and then we discuss the connection of the Pell-Pell p -sequence with Pell and Pell p -sequences.
Erdağ Özgür +2 more
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On a New Generalization of Pell Hybrid Numbers
Annales Mathematicae SilesianaeAbstract In this paper, we define and study a new one-parameter generalization of the Pell hybrid numbers. Based on the definition of r -Pell numbers, we define the r -Pell hybrid numbers.
Dorota Bród +2 more
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Generalized Pell’s equations and Weber’s class number problem
Journal de théorie des nombres de Bordeaux, 2023 We study a generalization of Pell’s equation, whose coefficients are certain algebraic integers. Let X 0 = 0
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On a new class of the generalized Gauss k-Pell numbers and their polynomials
Notes on Number Theory and Discrete Mathematics, 2022 In this article, we generalize the well-known Gauss Pell numbers and refer to them as generalized Gauss k-Pell numbers. There are relationships discovered between the class of generalized Gauss k-Pell numbers and the typical Gauss Pell numbers. Also, we generalize the known Gauss Pell polynomials, and call such polynomials as the generalized Gauss k ...
Kaya, Ahmet, Özimamoğlu, Hayrullah
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A New Generalization of Pell-Lucas Numbers (Bi-Periodic Pell-Lucas Sequence)
Communications in Mathematics and Applications, 2019 In this study, we bring into light, a new generalization of the Jacobsthal Lucas numbers, which shall also be called the bi-periodic Jacobsthal Lucas sequence as \begin{align*} Q_{n}= \begin{cases} 2bQ_{n-1}+Q_{n-2},&\text{if} \ n \ \text{is even} \\ 2aQ_{n-1}+Q_{n-2},&\text{if} \ n \ \text{is odd}% \end{cases} \text{\ \ }n\geq 2, \end{align*} with ...
Sukran Uygun, Hasan Karatas
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$k$-generalized Pell numbers which are repdigits in base $b$
Turkish Journal of Mathematics, 2022 Let $k\geq 2$ be an integer and let $(P_{n}^{(k)})_{n\geq 2-k}$ be the $k$ -generalized Pell sequence defined by \begin{equation*} P_{n}^{(k)}=2P_{n-1}^{(k)}+P_{n-2}^{(k)}+...+P_{n-k}^{(k)} \end{equation*} for $n\geq 2$ with initial conditions \begin{equation*} P_{-(k-2)}^{(k)}=P_{-(k-3)}^{(k)}=\cdot \cdot \cdot =P_{-1}^{(k)}=P_{0}^{(k)}=0,P_{1}^{(k ...
Şiar, Zafer, Keskin, Refik
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Regular polygonal numbers and generalized Pell equations [PDF]
International Mathematical Forum, 2007 In the eighteenth century, both square numbers and triangular num- bers were investigated by Euler and Goldbach (1742), who determined the recurrence relations satisfied by the sequence and established the general formulae explicitly. It seems to the author that the topics around this subject have not been touched in mathematical literature.
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On Generalized Third-Order Pell Numbers
Asian Journal of Advanced Research and Reports, 2019 In this paper, we investigate the generalized third order Pell sequences and we deal with, in detail, three special cases which we call them third order Pell, third order Pell-Lucas and modified third order Pell sequences. We present Binet’s formulas, generating functions, Simson formulas, and the summation formulas for these sequences.
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Properties of Generalized Fifth-Order Pell Numbers
Asian Research Journal of Mathematics, 2019 In this paper, we investigate the generalized fifth order Pell sequences and we deal with, in detail, three special cases which we call them as fifth order Pell, fifth order Pell-Lucas and modied fifth order Pell sequences.
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