# Balancing sequence contains no prime number

Shekh Mohammed Zahid

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 22, 2016, Number 4, Pages 25—28

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## Details

### Authors and affiliations

Shekh Mohammed Zahid

*Institute of Mathematics and Applications*

Bhubaneswar, Odisha, India

### Abstract

The study of prime number in any number sequence is crucial part. In recent year Panda and Behera introduced a new number sequence that is solutions of Diophantine equation 1 + 2 + 3 + … + (*n* – 1) = (*n* + 1) + (*n* + 2) + … + (*n* + *r*), where *n* and *r* are positive integers. The pairs (*n*, *r*) constitute a solution of above equation then *n* is called balancing number and *r* is the corresponding balancer. In this paper, we prove a main result that there is no prime number in the sequence of balancing numbers.

### Keywords

- Diophantine equation
- Balancing numbers
- Prime numbers
- Cobalancing numbers

### AMS Classification

### References

- Behera, A., & Panda, G. K. (1999) On the square roots of triangular numbers, Fibonacci Quarterly, 37, 98–105.
- Ray, P. K. (2009) Balancing and Cobalancing Numbers, http://www.nitrkl.ac.in/, http://ethesis.nitrkl.ac.in/2750/.
- Panda, G. K., & Ray, P. K. (2005) Cobalancing numbers and cobalancers, International Journal of Mathematics and Mathematical Sciences, 8, 1189–1200.
- Panda, G. K., and Ray, P. K. (2011) Some links of balancing and cobalancing numbers with Pell and associated Pell numbers, Bulletin of the Institute of Mathematics Academia Sinica (New Series), 6, 41–72.

## Related papers

## Cite this paper

APA
Zahid, S. M. (2016). Balancing sequence contains no prime number. Notes on Number Theory and Discrete Mathematics, 22(4), 25-28.

Chicago
Zahid, Shekh Mohammed. “Balancing Sequence Contains No Prime Number.” Notes on Number Theory and Discrete Mathematics 22, no. 4 (2016): 25-28.

MLA
Zahid, Shekh Mohammed. “Balancing Sequence Contains No Prime Number.” Notes on Number Theory and Discrete Mathematics 22.4 (2016): 25-28. Print.