Identities for balancing numbers using generating function and some new congruence relations

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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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 8n2 + 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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      Cite this paper

      APA

      Ray, 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.

      Chicago

      Ray, 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.

      MLA

      Ray, 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.

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