| Title:
|
Lucas balancing numbers (English) |
| Author:
|
Liptai, Kálmán |
| Language:
|
English |
| Journal:
|
Acta Mathematica Universitatis Ostraviensis |
| ISSN:
|
1214-8148 |
| Volume:
|
14 |
| Issue:
|
1 |
| Year:
|
2006 |
| Pages:
|
43-47 |
| . |
| Category:
|
math |
| . |
| Summary:
|
A positive $n$ is called a balancing number if \[1+2+\cdots +(n-1)=(n+1)+(n+2)+\cdots +(n+r).\] We prove that there is no balancing number which is a term of the Lucas sequence. (English) |
| Keyword:
|
Baker method |
| Keyword:
|
Pell equations |
| Keyword:
|
recurrence sequences |
| MSC:
|
11B39 |
| MSC:
|
11D45 |
| MSC:
|
11J86 |
| idZBL:
|
Zbl 1134.11005 |
| idMR:
|
MR2298912 |
| . |
| Date available:
|
2009-12-29T09:19:52Z |
| Last updated:
|
2013-10-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/137482 |
| . |
| Reference:
|
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| Reference:
|
[2] Baker A., Wüstholz G.: Logarithmic forms and group varieties., J. reine angew. Math., 442 (1993), 19–62. MR 1234835 |
| Reference:
|
[3] Behera A., Panda G. K.: On the square roots of triangular numbers., Fibonacci Quarterly, 37 No. 2 (1999), 98–105. Zbl 0962.11014, MR 1690458 |
| Reference:
|
[4] Ferguson D. E.: Letter to the editor., Fibonacci Quarterly, 8 (1970), 88–89. |
| Reference:
|
[5] Liptai K. : Fibonacci balancing numbers., Fibonacci Quarterly 42 (2004), 330–340. Zbl 1067.11006, MR 2110086 |
| Reference:
|
[6] Shorey T. N., Tijdeman R.: Exponential diophantine equations., Cambridge University Press, (1986). Zbl 0606.10011, MR 0891406 |
| Reference:
|
[7] Szalay L.: A note on the practical solution of simultaneous Pell type equations., submitted to Comp. Math. |
| . |
