Balancing and Lucas-Balancing Numbers and their Application to Cryptography
Computer Engineering and Applications Journal, 2016 It is well known that, a recursive relation for the sequence is an equation that relates to certain of its preceding terms . Initial conditions for the sequence are explicitly given values for a finite number of the terms of the sequence.
Sujata Swain +2 more
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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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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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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
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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
Bijan Kumar Patel +2 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.
Prasanta Kumar Ray
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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 ...
Prasanta Kumar Ray
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Boletim da Sociedade Paranaense de Matemática, 2011 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 ...
Prasanta Kumar Ray
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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 Salah Eddine Rihane
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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 $B_n$ and $C_n$ be the $n$-th balancing and Lucas-balancing numbers, respectively. We consider the Diophantine equations $ax+by=\frac{1}{2}(a-1)(b-1)$ and $1+ax+by=\frac{1}{2}(a-1)(b-1)$ for $(a,b)$ $\in$ $ \{(B_n,B_{n+1}),(B_{2n-1},B_{2n+1}), (B_n ...
Ravi Kumar Davala
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