Results 1 to 10 of about 1,369 (212)
On Balancing Quaternions and Lucas-Balancing Quaternions
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
doaj +5 more sources
On tridimensional Lucas-balancing numbers and some properties [PDF]
Notes on Number Theory and Discrete MathematicsIn this article, we introduce the tridimensional version of the Lucas-balancing numbers based on the unidimensional version, and we also study some of their properties and sum identities.
J. Chimpanzo +2 more
doaj +2 more sources
Almost balancers, almost cobalancers, almost Lucas-balancers and almost Lucas-cobalancers [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 In this work, the general terms of almost balancers, almost cobalancers, almost Lucas-balancers and almost Lucas-cobalancers of first and second type are determined in terms of balancing and Lucas-balancing numbers.
Ahmet Tekcan, Esra Zeynep Türkmen
doaj +1 more source
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 Bₙ and Cₙ be the n-th balancing and Lucas-balancing numbers, respectively. We consider the Diophantine equations ax + by = (1/2)(a - 1)(b - 1) and 1 + ax + by = (1/2)(a - 1)(b - 1) for (a,b) ∈ {(Bₙ,Bₙ₊₁), (B₂ₙ₋₁,B₂ₙ₊₁), (Bₙ,Cₙ), (Cₙ,Cₙ₊₁)} and ...
R. K. Davala
doaj +1 more source
On the Reciprocal Sums of Products of Balancing and Lucas-Balancing Numbers
Mathematics, 2021 Recently Panda et al. obtained some identities for the reciprocal sums of balancing and Lucas-balancing numbers. In this paper, we derive general identities related to reciprocal sums of products of two balancing numbers, products of two Lucas-balancing ...
Younseok Choo
doaj +1 more source
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
openaire +1 more source
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
doaj +1 more source
Two generalizations of dual-complex Lucas-balancing numbers
Acta Universitatis Sapientiae, Mathematica, 2022 AbstractIn 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. We give some of their properties, among others the Binet formula, Catalan, Cassini, d’Ocagne identities.
Bród Dorota +2 more
openaire +2 more sources
On $k$-Fibonacci balancing and $k$-Fibonacci Lucas-balancing numbers
Karpatsʹkì Matematičnì Publìkacìï, 2021 The balancing number $n$ and the balancer $r$ are solution of the Diophantine equation $$1+2+\cdots+(n-1) = (n+1)+(n+2)+\cdots+(n+r). $$ It is well known that if $n$ is balancing number, then $8n^2 + 1$ is a perfect square and its positive square root is
S.E. Rihane
doaj +1 more source
On the Properties of Balancing and Lucas-Balancing $p$-Numbers
Iranian Journal of Mathematical Sciences and Informatics, 2022 Summary: The main goal of this paper is to develop a new generalization of balancing and Lucas-balancing sequences namely balancing and Lucas-balancing \(p\)-numbers and derive several identities related to them. Some combinatorial forms of these numbers are also presented.
Behera, Adikanda, Ray, Prasanta Kumar
openaire +2 more sources