Table of Contents
Journal of Numbers
Volume 2014, Article ID 216738, 5 pages
Research Article

On Second Order Gap Balancing Numbers

Department of Mathematics, National Institute of Technology Rourkela, Odisha 769 008, India

Received 13 July 2014; Accepted 17 September 2014; Published 8 October 2014

Academic Editor: Jiyou Li

Copyright © 2014 S. S. Rout. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We consider the Diophantine equation for some natural numbers x, k, and r, and we call as kth order 2-gap balancing number. It was also proved that there are infinitely many first order 2-gap balancing numbers. In this paper, we show that the only second order 2-gap balancing number is 1.