Published Online: Jan 13, 2017
Page range: 15 - 21
Received: Dec 24, 2014
Accepted: Jun 26, 2015
DOI: https://doi.org/10.1515/udt-2016-0002
Keywords
© 2016 Prasanta Kumar Ray et al., published by De Gruyter Open
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.
The balancing numbers and the balancers were introduced by Behera et al. in the year 1999, which were obtained from a simple diophantine equation. The goal of this paper is to investigate the moduli for which all the residues appear with equal frequency with a single period in the sequence of balancing numbers. Also, it is claimed that, the balancing numbers are uniformly distributed modulo 2, and this holds for all other powers of 2 as well. Further, it is shown that the balancing numbers are not uniformly distributed over odd primes.