Results 11 to 20 of about 1,555,880 (294)
On the properties of k-balancing numbers [PDF]
Ain Shams Engineering Journal, 2018 In this study, a generalization of the sequence of balancing numbers called as k-balancing numbers is considered and some of their properties are established.
Prasanta Kumar Ray
exaly +5 more sources
On the Reciprocal Sums of Products of Balancing and Lucas-Balancing Numbers
Mathematics, 2021 Recently Panda et al. obtained some identities for the reciprocal sums of balancing and Lucas-balancing numbers. In this paper, we derive general identities related to reciprocal sums of products of two balancing numbers, products of two Lucas-balancing ...
Younseok Choo
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On Pell, Pell-Lucas, and balancing numbers [PDF]
Journal of Inequalities and Applications, 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 ...
Gül Karadeniz Gözeri
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On Harmonic Complex Balancing Numbers
Mathematics, 2022 In the present work, we define harmonic complex balancing numbers by considering well-known balancing numbers and inspiring harmonic numbers. Mainly, we investigate some of their basic characteristic properties such as the Binet formula and Cassini ...
Fatih Yılmaz +2 more
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On $k$-Fibonacci balancing and $k$-Fibonacci Lucas-balancing numbers
Karpatsʹkì Matematičnì Publìkacìï, 2021 The balancing number $n$ and the balancer $r$ are solution of the Diophantine equation $$1+2+\cdots+(n-1) = (n+1)+(n+2)+\cdots+(n+r). $$ It is well known that if $n$ is balancing number, then $8n^2 + 1$ is a perfect square and its positive square root is
S.E. Rihane
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Generalized Balancing and Balancing-Lucas numbers
Proyecciones (Antofagasta)In this paper, we introduce a generalization of Balancing and Balancing-Lucas numbers. We describe some of their properties also we give the related matrix representation and divisibility properties.
Al-Zoubi, Hasan, Al-Kateeb, Ala'a
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On the properties of k-balancing and k-Lucas-balancing numbers [PDF]
Acta et Commentationes Universitatis Tartuensis de Mathematica, 2017 The k-Lucas-balancing numbers are obtained from a special sequence of squares of k-balancing numbers in a natural form. In this paper, we will study some properties of k-Lucas-balancing numbers and establish relationship between these numbers and k-balancing numbers.
Prasanta Kumar Ray, Ray, Prasanta Kumar
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Solution to a pair of linear, two-variable, Diophantine equations with coprime coefficients from balancing and Lucas-balancing numbers [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 Let Bₙ and Cₙ be the n-th balancing and Lucas-balancing numbers, respectively. We consider the Diophantine equations ax + by = (1/2)(a - 1)(b - 1) and 1 + ax + by = (1/2)(a - 1)(b - 1) for (a,b) ∈ {(Bₙ,Bₙ₊₁), (B₂ₙ₋₁,B₂ₙ₊₁), (Bₙ,Cₙ), (Cₙ,Cₙ₊₁)} and ...
R. K. Davala
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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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Bidimensional extensions of balancing and Lucas-balancing numbers [PDF]
Journal of Discrete Mathematical Sciences & CryptographyIn this article bidimensional extensions of balancing and Lucas-balancing numbers are introduced, as well as some properties of these new bidimensional sequences.
Chimpanzo, J. +3 more
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