Subbalancing Numbers

Authors

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

DOI:

https://doi.org/10.11113/matematika.v34.n1.829

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

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Published

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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Articles