Trigonometric-type properties and the parity of balancing, Lucas-balancing, cobalancing and Lucas-cobalancing numbers [PDF]
MATEMATIKA, 2020 In recent year Panda and Behera introduced new integer sequnce called Balancing number. Panda and Ray modified integer sequnce to cobalancing number. Panda introduced corresponding Lucas-Balancing and cobalancing number. In this paper we insvestigate some new properties of lucas balancing and lucas cobalancing Number.
Ngô Văn Định
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On the Partial Finite Alternating Sums of Reciprocals of Balancing and Lucas-Balancing Numbers
Discussiones Mathematicae - General Algebra and Applications, 2020 In this note, the finite alternating sums of reciprocals of balancing and Lucas-balancing numbers are considered and several identities involving these sums are deduced.
Dutta Utkal Keshari, Ray Prasanta Kumar
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ON DUAL BICOMPLEX BALANCING AND LUCAS-BALANCING NUMBERS
Journal of Science and Arts, 2023 In this paper, dual bicomplex Balancing and Lucas-Balancing numbers are defined, and some identities analogous to the classic properties of the Fibonacci and Lucas sequences are produced. We give the relationship between these numbers and Pell and Pell-Lucas numbers.
Mıne Uysal +2 more
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On $${\pmb k}$$-Fibonacci numbers expressible as product of two Balancing or Lucas-Balancing numbers [PDF]
Indian Journal of Pure and Applied Mathematics, 2023 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Salah Eddine Rihane
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Balancing and Lucas-Balancing Numbers as the Difference of Two Repdigits [PDF]
13 pages.
Monalisa Mohapatra +2 more
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Sum formulas involving powers of balancing and Lucas-balancing numbers – II [PDF]
Notes on Number Theory and Discrete Mathematics, 2019 Summary: In this article, we obtain the closed form expressions for different types of summation formulas involving certain powers of balancing and Lucas-balancing numbers using the telescoping summation formula.
S. G. Rayaguru, G. K. Panda
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Certain Diophantine equations involving balancing and Lucas-balancing numbers
Acta et Commentationes Universitatis Tartuensis de Mathematica, 2016 It is well known that if x is a balancing number, then the positive square root of 8x2 + 1 is a Lucas-balancing number. Thus, the totality of balancing number x and Lucas-balancing number y are seen to be the positive integral solutions of the Diophantine equation 8x2 +1 = y2.
Prasanta Kumar Ray
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Repdigits as products of consecutive balancing or Lucas-balancing numbers [PDF]
The Fibonacci Quarterly, 2018 Repdigits are natural numbers formed by the repetition of a single digit. In this paper, we explore the presence of repdigits in the product of consecutive balancing or Lucas-balancing numbers.
S. G. Rayaguru, G. K. Panda
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On the Properties of Lucas-Balancing Numbers by Matrix Method [PDF]
Sigmae, 2014 Balancing 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.
Prasanta Kumar Ray
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Some Congruences for Balancing and Lucas-Balancing Numbers and Their Applications
, 2014 See the abstract in the attached pdf.
Prasanta Kumar Ray
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