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Bidimensional extensions of balancing and Lucas-balancing numbers [PDF]
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.
Chimpanzo, J. +3 more
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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 arithmetic functions of balancing and Lucas-balancing numbers [PDF]
Mathematical Communications, 2019 For any integers $n\geq1$ and $k\geq0,$ let $\phi(n)$ 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.
Dutta, Utkal Keshari +1 more
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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.
Ray, Prasanta Kumar
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Repdigits as difference of two balancing or Lucas-balancing numbers [PDF]
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Mohapatra, Monalisa +2 more
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Bidimensional Extensions of Cobalancing and Lucas-Cobalancing Numbers [PDF]
Annales Mathematicae Silesianae, 2023 A new bidimensional version of cobalancing numbers and Lucas-balancing numbers are introduced. Some properties and identities satisfied by these new bidimensional sequences are studied.
Chimpanzo J. +4 more
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The Solution of a System of Higher-Order Difference Equations in Terms of Balancing Numbers
Pan-American Journal of Mathematics, 2023 In this paper, we are interested in the closed-form solution of the following system of nonlinear difference equations of higher order, un+1 = 1/34-vn-m , vn+1 = 1/34-un-m, n, m ∈ N0, and the initial values u-j and v-j , j∈{0, 1, ..., m} are real numbers
Ahmed Ghezal, Imane Zemmouri
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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.
MINE UYSAL +2 more
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Fascinating Number Sequences from Fourth Order Difference Equation Via Quaternion Algebras
Discussiones Mathematicae - General Algebra and Applications, 2021 The balancing and Lucas-balancing numbers are solutions of second order recurrence relations. A linear combination of these numbers can also be obtained as solutions of a fourth order recurrence relation.
Patra Asim
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Solutions of the Diophantine Equations Br=Js+Jt and Cr=Js+Jt
Journal of Mathematics, 2023 Let Brr≥0, Jrr≥0, and Crr≥0 be the balancing, Jacobsthal, and Lucas balancing numbers, respectively. In this paper, the diophantine equations Br=Js+Jt and Cr=Js+Jt are completely solved.
Ahmed Gaber, Mohiedeen Ahmed
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