Results 1 to 10 of about 66,564 (179)
On Pell, Pell-Lucas, and balancing numbers. [PDF]
J Inequal Appl, 2018 In this paper, we derive some identities on Pell, Pell-Lucas, and balancing numbers and the relationships between them. We also deduce some formulas on the sums, divisibility properties, perfect squares, Pythagorean triples involving these numbers. Moreover, we obtain the set of positive integer solutions of some specific Pell equations in terms of the
Karadeniz Gözeri G.
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p-Analogue of biperiodic Pell and Pell–Lucas polynomials [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 In this study, a binomial sum, unlike but analogous to the usual binomial sums, is expressed with a different definition and termed the p-integer sum. Based on this definition, p-analogue Pell and Pell–Lucas polynomials are established and the generating
Bahar Kuloğlu +2 more
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On Hybrid Hyper k-Pell, k-Pell–Lucas, and Modified k-Pell Numbers
Axioms, 2023 Many different number systems have been the topic of research. One of the recently studied number systems is that of hybrid numbers, which are generalizations of other number systems.
Elen Viviani Pereira Spreafico +2 more
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Almost balancers, almost cobalancers, almost Lucas-balancers and almost Lucas-cobalancers [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 In this work, the general terms of almost balancers, almost cobalancers, almost Lucas-balancers and almost Lucas-cobalancers of first and second type are determined in terms of balancing and Lucas-balancing numbers.
Ahmet Tekcan, Esra Zeynep Türkmen
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On Mixed 𝐵-Concatenations of Pell and Pell–Lucas Numbers which are Pell Numbers [PDF]
Mathematica Pannonica, 2023 Let (𝑃𝑛)𝑛≥0 and (𝑄𝑛)𝑛≥0 be the Pell and Pell–Lucas sequences. Let 𝑏 be a positive integer such that 𝑏 ≥ 2. In this paper, we prove that the following two Diophantine equations 𝑃𝑛 = 𝑏𝑑𝑃𝑚 + 𝑄𝑘 and 𝑃𝑛 = 𝑏𝑑𝑄𝑚 + 𝑃𝑘 with 𝑑, the number of digits of 𝑃𝑘 or 𝑄𝑘 in base 𝑏, have only finitely many solutions in nonnegative integers (𝑚, 𝑛, 𝑘, 𝑏, 𝑑).
Adédji, Kouéssi Norbert +1 more
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Gaussian-bihyperbolic Numbers Containing Pell and Pell-Lucas Numbers
Journal of Advanced Research in Natural and Applied Sciences, 2023 In this study, we define a new type of Pell and Pell-Lucas numbers which are called Gaussian-bihyperbolic Pell and Pell-Lucas numbers. We also define negaGaussian-bihyperbolic Pell and Pell-Lucas numbers. Moreover, we obtain Binet’s formulas, generating function formulas, d’Ocagne’s identities, Catalan’s identities, Cassini’s identities and some sum ...
Hasan Gökbaş
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On Some Properties of Bihyperbolic Numbers of The Lucas Type
Communications in Advanced Mathematical Sciences, 2023 To date, many authors in the literature have worked on special arrays in various computational systems. In this article, Lucas type bihyperbolic numbers were defined and their algebraic properties were examined. Bihyperbolic Lucas numbers were studied by
Fügen Torunbalcı Aydın
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On Bicomplex Pell and Pell-Lucas Numbers
Communications in Advanced Mathematical Sciences, 2018 In this paper, bicomplex Pell and bicomplex Pell-Lucas numbers are defined. Also, negabicomplex Pell and negabicomplex Pell-Lucas numbers are given. Some algebraic properties of bicomplex Pell and bicomplex Pell-Lucas numbers which are connected between ...
Fügen Torunbalcı Aydın
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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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Non-Newtonian Pell and Pell-Lucas numbers
Journal of New Results in ScienceIn the present paper, we introduce a new type of Pell and Pell-Lucas numbers in terms of non-Newtonian calculus, which we call non-Newtonian Pell and non-Newtonian Pell-Lucas numbers, respectively.
Tülay Yağmur
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