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Diophantine equations concerning balancing and Lucas balancing numbers
Archiv Der Mathematik, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Sudhansu Sekhar Rout, Pallab Kanti Dey
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Octonions and hyperbolic octonions with the k-balancing and k-Lucas balancing numbers
Journal of AnalysisIn this paper, the authors defined the \(k\)-balancing and \(k\)-Lucas balancing octonions and hyperbolic octonions. For \(n\geq 0\), the \(n^{th}\) \(k\)-balancing octonions \(\{B\mathbb{Q}_{k,n}\}\) and the \(n^{th}\) \(k\)-Lucas balancing octonions \(\{C\mathbb{Q}_{k,n}\}\) are defined \[ B\mathbb{Q} _{k,n}=B_{k,n}e_{0}+B_{k,n+1}e_{1}+B_{k,n+2}e_{2}+
Jagmohan Tanti +2 more
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Exact Divisibility by Powers of the Balancing and Lucas-Balancing Numbers
The Fibonacci Quarterly, 2021Asim Patra
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Brousseau’s Reciprocal Sums Involving Balancing and Lucas-Balancing Numbers
The Journal of the Indian Mathematical Society, 2022In this paper, we derive the closed form expressions for the finite and infinite sums with summands having products of balancing and Lucas-balancing numbers in the denominator. We present some generalized Brousseau’s sums for balancing and Lucas-balancing numbers.
Rayaguru, S. G., Panda, G. K.
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INCOMPLETE BALANCING AND LUCAS-BALANCING NUMBERS
2018The aim of this article is to establish some combinatorial expressions of balancing and Lucas-balancing numbers and investigate some of their properties.
Patel, Bijan Kumar +2 more
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On the Properties of Lucas-Balancing Numbers by Matrix Method
Sigmae, 2014Balancing numbers n and balancers r are originally dened as the solution of the Diophantine equation 1 + 2 + ... + (n - 1) = (n + 1) + (n + 2) + ... + (n + r). If n is a balancing number, then 8n^2 +1 is a perfect square. Further, If n is a balancing number then the positive square root of 8n^2 + 1 is called a Lucas-balancing number.
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Balancing and Lucas-Balancing hybrid numbers and some identities
Journal of Information and Optimization SciencesIn this paper, we introduce Balancing and Lucas-Balancing hybrid numbers. We examine some identities of Balancing and Lucas-Balancing hybrid numbers. We give some basic definitions and properties related to them. In addition, we find Binet’s Formula, Cassini’s identity, Catalan’s identity, d’Ocagne identity, generating functions, exponential generating
Mine Uysal, Engin Özkan
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Spinor algebra of k-balancing and k-Lucas-balancing numbers
Journal of Algebra and Its ApplicationsIn this paper, we introduce and study a spinor algebra of [Formula: see text]-balancing numbers referred to as the [Formula: see text]-balancing and [Formula: see text]-Lucas-balancing spinors. First, we give [Formula: see text]-balancing quaternions and their some algebraic properties. Then we introduce a spinor family of [Formula: see text]-balancing
Kalika Prasad +3 more
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New Hybrid Numbers with Balancing and Lucas-Balancing Number Components
2023Nurkan, Semra +3 more
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