Derivation and Applications of a Formula for Balancing Numbers Using Range Endpoints
Year: 2025
Type: article
Abstract: This paper presents a mathematical derivation of a formula to determine the balancing number x within a given range [A, L]. A balancing number is a unique integer in the range that equally partitions the sum of integers on both sides. The method relies solely on the starting A and ending L numbers, eliminating the need for a balancer. This efficient approach is validated with examples and visualizations, showcasing its accuracy and potential applications in resource allocation and optimization. Keywords: Balancing Numbers, Number Theory, Optimization, Math, Data Visualization, Diophantine Equations
Author: Sakibur Rahman Utshow
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6949527648
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