| Title:
|
On the Diophantine equation $x^{2}-kxy+y^{2}-2^{n}=0$ (English) |
| Author:
|
Keskin, Refik |
| Author:
|
Şiar, Zafer |
| Author:
|
Karaatlı, Olcay |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
63 |
| Issue:
|
3 |
| Year:
|
2013 |
| Pages:
|
783-797 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this study, we determine when the Diophantine equation $x^{2}-kxy+y^{2}-2^{n}=0$ has an infinite number of positive integer solutions $x$ and $y$ for $0\leq n\leq 10.$ Moreover, we give all positive integer solutions of the same equation for $0\leq n\leq 10$ in terms of generalized Fibonacci sequence. Lastly, we formulate a conjecture related to the Diophantine equation $x^{2}-kxy+y^{2}-2^{n}=0$. (English) |
| Keyword:
|
Diophantine equation |
| Keyword:
|
Pell equation |
| Keyword:
|
generalized Fibonacci number |
| Keyword:
|
generalized Lucas number |
| MSC:
|
11B37 |
| MSC:
|
11B39 |
| MSC:
|
11B50 |
| MSC:
|
11B99 |
| idZBL:
|
Zbl 06282110 |
| idMR:
|
MR3125654 |
| DOI:
|
10.1007/s10587-013-0052-y |
| . |
| Date available:
|
2013-10-07T12:08:41Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143489 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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