Results 21 to 30 of about 51,391 (253)
On arithmetic functions of balancing and Lucas-balancing numbers
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.
Dutta, Utkal Keshari +3 more
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Indian Journal of Pure and Applied Mathematics, 2023 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
S. Rihane
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Certain matrices associated with balancing and Lucas-balancing numbers
, 2012 Balancing numbers $n$ and balancers $r$ are originally defined as the solution of the Diophantine equation $1+2+cdots+(n-1)=(n+1)+(n+2)+cdots+(n+r)$. These numbers can be generated by the linear recurrence $B_{n+1}=6B_{n}-B_{n-1}$ or by the nonlinear ...
Husna Zayadi
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Repdigits as difference of two balancing or Lucas-balancing numbers
Repdigits are natural numbers formed by the repetition of a single digit. In this paper, we study the problem of writing repdigits as the difference of two balancing or Lucas-balancing numbers.
Panda, Gopal Krishna +2 more
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On Balancing and Lucas-balancing Quaternions [PDF]
, 2021 summary:The aim of this article is to investigate two new classes of quaternions, namely, balancing and Lucas-balancing quaternions that are based on balancing and Lucas-balancing numbers, respectively. Further, some identities including Binet's formulas,
Patel, Bijan Kumar, Ray, Prasanta Kumar
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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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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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Journal of Innovative Applied Mathematics and Computational Sciences, 2021 In this paper, closed forms of the sum formulas $\sum_{k=0}^{n}x^{k}W_{mk+j}^{2}$ for generalized balancing numbers are presented. As special cases, we give sum formulas of balancing, modified Lucas-balancing and Lucas-balancing numbers.
Yüksel Soykan +2 more
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Mersenne-Horadam identities using generating functions
Karpatsʹkì Matematičnì Publìkacìï, 2020 The main object of the present paper is to reveal connections between Mersenne numbers $M_n=2^n-1$ and generalized Fibonacci (i.e., Horadam) numbers $w_n$ defined by a second order linear recurrence $w_n=pw_{n-1}+qw_{n-2}$, $n\geq 2$, with $w_0=a$ and ...
R. Frontczak, T.P. Goy
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