Certain Diophantine equations involving balancing and Lucas-balancing numbers

Prasanta Kumar Ray

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.

Keywords


balancing numbers; Lucas-balancing numbers; Diophantine equations

Full Text:

PDF


DOI: http://dx.doi.org/10.12697/ACUTM.2016.20.14

Refbacks

  • There are currently no refbacks.




ISSN 1406–2283 (print)
ISSN 2228–4699 (online)