Original scientific paper

On Diophantine, pronic and triangular triples of balancing numbers

Sai Gopal Rayaguru orcid.org/0000-0003-2575-4768 ; Department of Mathematics, National Institute of Technology Rourkela, Orissa , India
Gopal Krishna Panda ; Department of Mathematics, National Institute of Technology Rourkela, Orissa , India
Alain Togbe ; Department of Mathematics, Statistics and Computer Science, Purdue University Northwest, USA

Abstract

In this paper, we search for some Diophantine triples of balancing numbers. We prove that, if $(6\pm2)B_nB_k+1$ and $(6\pm2)B_{n+2}B_k+1$ are both perfect squares then $k=n+1$, for any positive integer $n \geq 1$. In addition, we define pronic $m$-tuples, triangular $m$-tuples and prove some results related to pronic and triangular triples of balancing numbers.

Keywords

Balancing numbers; Diophantine triples; Linear forms in complex and $p$-adic logarithms

Hrčak ID:

235566

URI

https://hrcak.srce.hr/235566

Publication date:

12.3.2020.

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