Some links of balancing and cobalancing numbers with Pell and associated Pell numbers
by G. K. Panda   Prasanta Kumar Ray  

Vol. 6 No. 1 (2011) P.41~P.72

ABSTRACT

Links of balancing and cobalancing numbers with Pell and associated Pell numbers are established. It is proved that the $n^{th}$ balancing number is product of the $n^{th}$ Pell number and the $n^{th}$ associated Pell number. It is further observed that the sequences of balancing and cobalancing numbers are very closely related to the Pell sequence whereas, the sequences of Lucas-balancing and Lucas-cobalancing numbers constitute the associated Pell sequence. The solutions of some Diophantine equations including Pythagorean and Pythagorean-type equations are obtained in terms of these numbers.

KEYWORDS
Triangular numbers, Pronic numbers, balancing numbers, cobalancing numbers, Lucas-balancing numbers, Lucas-cobalancing numbers, balancers, cobalancers, Pell numbers, associated Pell numbers, recurrence relations, Pell's equation

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 11B37, 11B83, 11D04, 11D09

MILESTONES

Received: 2009-04-28
Revised : 2009-09-25
Accepted: 2009-09-25

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