Results 11 to 20 of about 47,656 (155)
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
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Certain Diophantine equations involving balancing and Lucas-balancing numbers [PDF]
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 difference of two balancing or Lucas-balancing numbers [PDF]
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Monalisa Mohapatra +2 more
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Application of Chybeshev Polynomials in Factorizations of Balancing and Lucas-Balancing Numbers
Boletim da Sociedade Paranaense de Matemática, 2012 In this paper, with the help of orthogonal polynomial especially Chybeshev polynomials of first and second kind, number theory and linear algebra intertwined to yield factorization of the balancing and Lucas-balancing numbers.
Prasanta Kumar Ray
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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 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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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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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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Bidimensional extensions of balancing and Lucas-balancing numbers
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.
J. Chimpanzo +3 more
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Positive Integer Solutions of Certain Diophantine Equations Involving Lucas-Balancing numbers
, 2018 There is some technical problems and issues with some of the contents of the paper, so I want to withdraw the ...
Asim Patra
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