Article
Uniform Distribution of the Sequence of Balancing Numbers Modulo M
Authors
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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 bal- ancing 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.
Keywords
Balancing numbers, Balancers, Uniform distribution, Periodicity of balancing.
Citation
Ray, P. K. & Patel, B. K. (2016). Uniform distribution of the sequence of balancing numbers modulo m. Uniform Distribution Theory, 11(1), 15–21. https://doi.org/10.1515/udt-2016-0002
P. K. Ray and B. K. Patel, “Uniform distribution of the sequence of balancing numbers modulo m,” Uniform Distribution Theory, vol. 11, no. 1, pp. 15–21, 2016, doi: 10.1515/udt-2016-0002.
Ray PK, Patel BK. Uniform distribution of the sequence of balancing numbers modulo m. Uniform Distribution Theory. 2016;11(1):15–21. doi:10.1515/udt-2016-0002.
Ray, P. K. and Patel, B. K. (2016), ‘Uniform distribution of the sequence of balancing numbers modulo m’, Uniform Distribution Theory, 11(1), pp. 15–21. Available at: https://doi.org/10.1515/udt-2016-0002.
Ray, Prasanta Kumar, and Bijan Kumar Patel. “Uniform Distribution of the Sequence of Balancing Numbers Modulo M.” Uniform Distribution Theory, vol. 11, no. 1, 2016, pp. 15–21. https://doi.org/10.1515/udt-2016-0002.
Ray, Prasanta Kumar, and Bijan Kumar Patel. “Uniform Distribution of the Sequence of Balancing Numbers Modulo M.” Uniform Distribution Theory 11, no. 1 (2016): 15–21. https://doi.org/10.1515/udt-2016-0002.
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Published by: Engineering Journals
