<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></abstract>

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.

Uniform Distribution of the Sequence of Balancing Numbers Modulo <italic>m</italic>

Department of Mathematics, Veer Surendra Sai University of Technology, Burla, Sambalpur-768018,

Department of Mathematics, International Institute of Information Technology, Bhubaneswar-751003,

Uniform distribution theory

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Uniform Distribution of the Sequence of Balancing Numbers Modulo 

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...

Uniform Distribution of the Sequence of Balancing Numbers Modulo m

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
Balancing numbers, Balancers, Uniform distribution, Periodicity of balancing numbers

© 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.

Uniform Distribution of the Sequence of Balancing Numbers Modulo m

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

KeywordsBalancing numbers, Balancers, Uniform distribution, Periodicity of balancing numbers

© 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.

Keywords
Balancing numbers, Balancers, Uniform distribution, Periodicity of balancing numbers