Prasanta K Ray, Sunima Patel and Manoj K Mandal

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 22, 2016, Number 4, Pages 41—48

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## Details

### Authors and affiliations

Prasanta K Ray

*Veer Surendra Sai University of Technology
Odisha, Burla, India*

Sunima Patel

*National Institute of Technology
Rourkela, India*

Manoj K Mandal

*National Institute of Technology
Rourkela, India*

### Abstract

It is well-known that the balancing numbers are the square roots of the triangular numbers and are the solutions of the Diophantine equation 1 + 2 + … + (*n* − 1) = (*n* + 1) + (*n* + 2) + … + (*n* + *r*), where *r* is the balancer corresponding to the balancing number *n*. Thus if *n* is a balancing number, then 8*n*^{2} + 1 is a perfect square and its positive square root is called a Lucas-balancing number. The goal of this paper is to establish some new identities of these numbers.

### Keywords

- Generating function
- Balancing
- Congruence

### AMS Classification

- 11B39
- 11B83

### References

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## Related papers

## Cite this paper

APARay, P.K., Patel, S. & Mandal, M. K. (2016). Identities for balancing numbers using generating function and some new congruence relations, Notes on Number Theory and Discrete Mathematics, 22(4), 41-48.

ChicagoRay, Prasanta K., Sunima Patel and Manoj K Mandal “Identities for Balancing Numbers Using Generating Function and Some New Congruence Relations.” Notes on Number Theory and Discrete Mathematics 22, no. 4 (2016): 41-48.

MLARay, Prasanta K., Sunima Patel and Manoj K Mandal, “Identities for Balancing Numbers Using Generating Function and Some New Congruence Relations.”Notes on Number Theory and Discrete Mathematics 22.4 (2016): 41-48. Print.