# Subbalancing Numbers

## Authors

• Ravi Kumar Davala National Institute of Technology, Rourkela, India
• G. K. Panda National Institute of Technology, Rourkela, India

## Abstract

A natural number \$n\$ is called balancing number (with balancer \$r\$)if it satisfies the Diophantine equation \$1+2+\cdots+(n-1)=(n+1)+(n+2)+\cdots+(n+r).\$ However, if for some pair of natural numbers \$(n,r)\$, \$1+2+\cdots+(n-1) < (n+1)+(n+2)+\cdots+(n+r)\$ and equality is achieved after adding a natural number \$D\$ to the left hand side then we call \$n\$ a \$D\$-subbalancing number with \$D\$-subbalaner number \$r\$. In this paper, such numbers are studied for certain values of \$D\$.

## Author Biography

### Ravi Kumar Davala, National Institute of Technology, Rourkela, India

Department of Mathematics

2018-05-28

## How to Cite

Davala, R. K., & Panda, G. K. (2018). Subbalancing Numbers. MATEMATIKA: Malaysian Journal of Industrial and Applied Mathematics, 34(1), 163–171. https://doi.org/10.11113/matematika.v34.n1.829

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