Results 11 to 20 of about 1,995,314 (144)
On the Partial Finite Alternating Sums of Reciprocals of Balancing and Lucas-Balancing Numbers [PDF]
Discussiones Mathematicae - General Algebra and Applications, 2020 In this note, the finite alternating sums of reciprocals of balancing and Lucas-balancing numbers are considered and several identities involving these sums are deduced.
Dutta Utkal Keshari, Ray Prasanta Kumar
doaj +4 more sources
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 properties.
Patel, Bijan Kumar +2 more
core +8 more sources
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, Ray, Prasanta Kumar
openaire +4 more sources
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
openaire +3 more sources
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
doaj +2 more sources
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
openaire +4 more sources
A note on k-tridiagonal matrices with the balancing and Lucas-balancing numbers.
Ars Comb., 2015 In this note, we consider one type of k-tridiagonal matrix family whose permanents and determinants are specified to the balancing and Lucas-balancing numbers. Moreover, we provide some properties between Chebyshev polynomial properties and the given number sequences.
Yilmaz, Fatih, Kirklar, Emrullah
core +6 more sources
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
core +4 more sources
Repdigits as difference of two balancing or Lucas-balancing numbers [PDF]
12
Mohapatra, Monalisa +2 more
core +4 more sources
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