Certain Diophantine equations involving balancing and Lucas-balancing numbers

  • Prasanta Kumar Ray Veer Surendra Sai University of Technology, Odisha, Burla-768018
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.
Published
2016-12-02
Section
Articles