Certain Diophantine equations involving balancing and Lucas-balancing numbers

Authors

  • Prasanta Kumar Ray Veer Surendra Sai University of Technology, Odisha, Burla-768018

DOI:

https://doi.org/10.12697/ACUTM.2016.20.14

Keywords:

balancing numbers, Lucas-balancing numbers, Diophantine equations

Abstract

It is well known that if x is a balancing number, then the positive square root of 8x2 + 1 is a Lucas-balancing number. Thus, the totality of balancing number x and Lucas-balancing number y are seen to be the positive integral solutions of the Diophantine equation 8x2 +1 = y2. In this article, we consider some Diophantine equations involving balancing and Lucas-balancing numbers and study their solutions.

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Published

2016-12-02

Issue

Section

Articles