2011 / March Volume 6 No.1
Some links of balancing and cobalancing numbers with Pell and associated Pell numbers
| Published Date |
2011 / March
|
|---|---|
| Title | Some links of balancing and cobalancing numbers with Pell and associated Pell numbers |
| Author | |
| Keyword |
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, 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
|
| Download | |
| Pagination | 41-72 |
| 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.
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| AMS Subject Classification |
11B37, 11B83, 11D04, 11D09
|
| Received |
2009-09-25
|
| Accepted |
2009-09-25
|