Results 11 to 20 of about 51,391 (253)
On Balancing Quaternions and Lucas-Balancing Quaternions [PDF]
Discussiones Mathematicae - General Algebra and Applications, 2021 In this paper we define and study balancing quaternions and Lucas-balancing quaternions. We give the generating functions, matrix generators and Binet formulas for these numbers. Moreover, the well-known properties e.g. Catalan, d’ Ocagne identities have
Bród Dorota
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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 ...
Prasanta Kumar Ray, Ray, Prasanta Kumar
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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 ...
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.
M. Uysal, E. Özkan, Anthony G. Shannon
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Two generalizations of dual-complex Lucas-balancing numbers
Acta Universitatis Sapientiae, Mathematica, 2022 In this paper, we study two generalizations of dual-complex Lucas-balancing numbers: dual-complex k-Lucas balancing numbers and dual-complex k-Lucas-balancing numbers.
D. Bród, A. Szynal-Liana, I. Włoch
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INCOMPLETE BALANCING AND LUCAS-BALANCING NUMBERS [PDF]
, 2018 The aim of this article is to establish some combinatorial expressions of balancing and Lucas-balancing numbers and investigate some of their ...
Patel, Bijan Kumar +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, 2018 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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Factorizations of the Negatively Subscripted Balancing and Lucas-Balancing Numbers
Boletim da Sociedade Paranaense de Matemática, 2013 In this paper, we find some tridigonal matrices whose determinant and permanent are equal to the negatively subscripted balancing and Lucas- balancing numbers.
P. Ray
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TRIGONOMETRIC-TYPE IDENTITIES AND THE PARITY OF BALANCING AND LUCAS-BALANCING NUMBERS [PDF]
TNU Journal of Science and Technology, 2021 Các số cân bằng n được định nghĩa như là nghiệm của phương trình Diophantus 1 + 2 + · · · + (n − 1) = (n + 1) + · · · + (n + r), trong đó r được gọi là hệ số cân bằng ứng với số cân bằng n.
Ngô Văn Định
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Period of balancing numbers modulo product of consecutive Lucas-balancing numbers
MATHEMATICA, 2018 The period of the balancing numbers modulo m, denoted by π(m), is the least positive integer l such that {Bl, Bl+1} ≡ {0, 1} (mod m), where Bl denotes the l-th balancing number. In the present study, we examine the periods of the balancing numbers modulo
B. Patel, S. K. Sunanda, P. Ray
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