Perfect squares in the sum and difference of balancing-like numbers

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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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


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 G_{n+1}=AG_n-G_{n-1} with initial terms G_0=0,G_1=1 for A \geq 3.


  • Sum of divisors
  • Perfect numbers

2020 Mathematics Subject Classification

  • 11A25


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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

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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.

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