**M. K. Sahukar, Zafer Şiar, Refik Keskin and G. K. Panda**

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 28, 2022, Number 2, Pages 286–301

DOI: 10.7546/nntdm.2022.28.2.286-301

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## Details

### Authors and affiliations

**M. K. Sahukar**

*Department of Mathematics, National Institute of Technology
Rourkela, Orissa, India*

**Zafer Şiar**

*Department of Mathematics, Bingöl University
Bingöl, Turkey*

**Refik Keskin**

*Department of Mathematics, Bingöl University
Bingöl, Turkey*

**G. K. Panda**

*Department of Mathematics, National Institute of Technology
Rourkela, Orissa, India*

### Abstract

In this study, we deal with the existence of perfect powers which are sum and difference of two balancing numbers. Moreover, as a generalization we explore the perfect squares which are sum and difference of two balancing-like numbers, where balancing-like sequence is defined recursively as with initial terms for .

### Keywords

- Sum of divisors
- Perfect numbers

### 2020 Mathematics Subject Classification

- 11A25

### References

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### Manuscript history

- Received: 23 September 2021
- Revised: 23 April 2022
- Accepted: 5 May 2022
- Online First: 12 May 2022
- Corrected Version: 20 May 2022

## Related papers

## Cite this paper

Sahukar, M. K., Şiar, Z., Keskin, R., & Panda, G. K. (2022). Perfect squares in the sum and difference of balancing-like numbers. *Notes on Number Theory and Discrete Mathematics*, 28(2), 286-301, DOI: 10.7546/nntdm.2022.28.2.286-301.