منابع مشابه
On Pell, Pell-Lucas, and balancing numbers
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 integer sequences mentioned in the text.
متن کاملThe sum and product of Fibonacci numbers and Lucas numbers, Pell numbers and Pell-Lucas numbers representation by matrix method
Denote by {Fn} and {Ln} the Fibonacci numbers and Lucas numbers, respectively. Let Fn = Fn × Ln and Ln = Fn + Ln. Denote by {Pn} and {Qn} the Pell numbers and Pell-Lucas numbers, respectively. Let Pn = Pn × Qn and Qn = Pn + Qn. In this paper, we give some determinants and permanent representations of Pn, Qn, Fn and Ln. Also, complex factorization formulas for those numbers are presented. Key–Wo...
متن کاملOn the intersections of Fibonacci, Pell, and Lucas numbers
We describe how to compute the intersection of two Lucas sequences of the forms {Un(P,±1)}n=0 or {Vn(P,±1)} ∞ n=0 with P ∈ Z that includes sequences of Fibonacci, Pell, Lucas, and Lucas-Pell numbers. We prove that such an intersection is finite except for the case Un(1,−1) and Un(3, 1) and the case of two V-sequences when the product of their discriminants is a perfect square. Moreover, the int...
متن کاملOn the Properties of Balancing and Lucas-Balancing $p$-Numbers
The main goal of this paper is to develop a new generalization of balancing and Lucas-balancing sequences namely balancing and Lucas-balancing $p$-numbers and derive several identities related to them. Some combinatorial forms of these numbers are also presented.
متن کاملk-Pell, k-Pell-Lucas and Modified k-Pell Numbers: Some Identities and Norms of Hankel Matrices
In this paper we present some identities involving terms of k-Pell, k-Pell-Lucas and Modified k-Pell sequences. We also give some results on the column and row norms of Hankel matrices which entries are numbers of these sequences. Mathematics Subject Classification: 11B37, 11B83, 15A60
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ژورنال
عنوان ژورنال: Journal of Physics: Conference Series
سال: 2019
ISSN: 1742-6588,1742-6596
DOI: 10.1088/1742-6596/1344/1/012017