| Title:
|
The diophantine equation $x^2+2^a\cdot 17^b=y^n$ (English) |
| Author:
|
Gou, Su |
| Author:
|
Wang, Tingting |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
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62 |
| Issue:
|
3 |
| Year:
|
2012 |
| Pages:
|
645-654 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $\mathbb {Z}$, $ \mathbb {N}$ be the sets of all integers and positive integers, respectively. Let $p$ be a fixed odd prime. Recently, there have been many papers concerned with solutions $(x, y, n, a, b)$ of the equation $ x^2+2^ap^b=y^n$, $x, y, n\in \mathbb {N}$, $\gcd (x, y)=1$, $n\geq 3$, $a, b\in \mathbb {Z}$, $a\geq 0$, $b\geq 0. $ And all solutions of it have been determined for the cases $p=3$, $p=5$, $p=11$ and $p=13$. In this paper, we mainly concentrate on the case $p=3$, and using certain recent results on exponential diophantine equations including the famous Catalan equation, all solutions $(x, y, n, a, b)$ of the equation $x^2+2^a\cdot 17^b=y^n$, $x, y, n\in \mathbb {N}$, $\gcd (x, y)=1$, $n\geq 3$, $a, b\in \mathbb {Z}$, $ a\geq 0$, $ b\geq 0$, are determined. (English) |
| Keyword:
|
exponential diophantine equation |
| Keyword:
|
modular approach |
| Keyword:
|
arithmetic properties of Lucas numbers |
| MSC:
|
11D61 |
| idZBL:
|
Zbl 1265.11062 |
| idMR:
|
MR2984625 |
| DOI:
|
10.1007/s10587-012-0056-z |
| . |
| Date available:
|
2012-11-10T21:03:24Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143016 |
| . |
| Reference:
|
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