IJPAM: Volume 85, No. 3 (2013)

NEW IDENTITIES FOR THE COMMON FACTORS OF
BALANCING AND LUCAS-BALANCING NUMBERS

Prasanta Kumar Ray
International Institute of Information Technology
Gothapatna, PO: MALIPADA, Bhubaneswar,751 003, INDIA


Abstract. Balancing numbers n and balancers r are originally defined as the solution of the Diophantine equation 1+2+...+(n-1)=(n+1)+(n+2)+...+(n+r). If n is a balancing number, then 8n2+1 is a perfect square. Further, If n is a balancing number then the positive square root of 8n2+1 is called a Lucas-balancing number. These numbers can be generated by the linear recurrences Bn+1=6Bn-Bn-1 and Cn+1=6Cn-Cn-1 where Bn and Cn are respectively denoted by the n-th balancing number and n-th Lucas-balancing number. In this study, we establish some new identities for the common factors of both balancing and Lucas-balancing numbers.

Received: January 11, 2013

AMS Subject Classification: 11B39, 11B83

Key Words and Phrases: balancing numbers, Lucas-balancing numbers, recurrence relation

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DOI: 10.12732/ijpam.v85i3.5 How to cite this paper?
Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 85
Issue: 3