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On the Periodicity of Lucas-Balancing Numbers and p-adic Order of Balancing Numbers
Iranian Journal of Science and Technology Transaction A: Science, 2020The objective of this article is to study the periodicity of Lucas-balancing numbers modulo any positive integer. Some relations between the periodicity of balancing and Lucas-balancing numbers are also discussed. Further, in this study the p-adic order of balancing numbers is completely characterized .
Takao Komatsu, Bijan Kumar Patel
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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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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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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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On kk{\pmb k}-Fibonacci numbers expressible as product of two Balancing or Lucas-Balancing numbers
Indian Journal of Pure and Applied Mathematics, 2023Salah Eddine Rihane
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Some properties of r-circulant matrices with k-balancing and k-Lucas balancing numbers
Boletin De La Sociedad Matematica Mexicana, 2023Kalika Prasad +2 more
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