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A note on the generalized bi-periodic Lucas-balancing numbers

BRAZILIAN ELECTRONIC JOURNAL OF MATHEMATICS
In this study, we introduce a new class of integers called the sequence of generalized bi-periodic Lucas-balancing numbers, which extends the well-known sequence of Lucas-balancing numbers. We present several fundamental properties, including the deduction of the corresponding generating function, as well as homogeneous and non-homogeneous recurrence ...
Eudes Antônio Costa, Elen Viviani Pereira Spreafico, Paula Catarino   +2 more
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Repdigits as difference of two balancing or Lucas-balancing numbers [PDF]

12
Monalisa Mohapatra, Pritam Kumar Bhoi, G. K. Panda   +2 more
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On the properties of k-balancing and k-Lucas-balancing numbers

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
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On arithmetic functions of balancing and Lucas-balancing numbers

Mathematical Communications, 2019
Summary: For any integers \(n\ge 1\) and \(k\ge 0,\) let \(\varphi(n)\) and \(\sigma_{k}(n)\) denote the Euler phi-function and the sum of the \(k\)-th powers of the divisors of \(n\), respectively. In this article, the solutions to some Diophantine equations about these functions of balancing and Lucas-balancing numbers are discussed.
Utkal Keshari Dutta, Prasanta Kumar Ray
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Positive Integer Solutions of Certain Diophantine Equations Involving Lucas-Balancing numbers [PDF]

, 2018
There is some technical problems and issues with some of the contents of the paper, so I want to withdraw the ...
Asim Patra
  +5 more sources

Hybrid numbers with balancing and Lucas balancing hybrid number coefficients

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics
In this note, we made a connection between hybrid numbers and hybrid balancing, and hybrid Lucas balancing number. Initially, we obtained for these new number recurrence relation, some important relations among new numbers, and Binet's like formula.
Murat Turan, Sıddıka Özkaldı Karakuş   +1 more
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Bidimensional extensions of balancing and Lucas-balancing numbers

Journal of Discrete Mathematical Sciences & Cryptography
In this article bidimensional extensions of balancing and Lucas-balancing numbers are introduced, as well as some properties of these new bidimensional sequences.
J. Chimpanzo, Paula Catarino, Paulo Vasco, A. Borges   +3 more
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NEW IDENTITIES FOR THE COMMON FACTORS OF BALANCING AND LUCAS-BALANCING NUMBERS [PDF]

International Journal of Pure and Apllied Mathematics, 2013
Balancing numbers n and balancers r are originally defined 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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Application of Chybeshev Polynomials in Factorizations of Balancing and Lucas-Balancing Numbers

Boletim da Sociedade Paranaense de Matemática, 2012
Summary: In this paper, with the help of orthogonal polynomials especially Chybeshev polynomials of first and second kind, number theory and linear algebra intertwined to yield factorization of balancing and Lucas-balancing numbers.
Prasanta Kumar Ray
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On balancing and Lucas-balancing numbers expressible as product of two $k$-Fibonacci numbers [PDF]

A positive integer $n$ is called a balancing number if there exists a positive integer $r$ such that $1 + 2 + \cdots + (n-1) = (n+1) + (n+2) + \cdots + (n+r)$. The corresponding value $r$ is known as the balancer of $n$. If $n$ is a balancing number, then $8n^{2}+1$ is a perfect square, and its positive square root is called a Lucas-balancing number ...
Bibhu Prasad Tripathy, Bijan Kumar Patel
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