Year: 2025
Type: article
Abstract: In this paper we discuss some aspects and properties of Balancing Numbers and some other related numbers. We prove, among other things, that a balancing number cannot be a power of a prime integer. We give some identities concerning these numbers and its related numbers. We use linear algebra techniques to write a balancing number and its related numbers in the Binet form. Key words and phrases. Balancing numbers, balancers, balancing matrices, Binet form, Diophantine equation, Lucas-balancing numbers, Pell’s equation. 2020 Mathematics Subject Classification. 11A05; 11B37; 11B39; 11B83
Author: Jebrel M. Habeb
Institution: Yarmouk University
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W7220546604