IJPAM: Volume 85, No. 3 (2013)
BALANCING AND LUCAS-BALANCING NUMBERS
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