| Title:
|
On the diophantine equation $x^2+2^a3^b73^c=y^n $ (English) |
| Author:
|
Alan, Murat |
| Author:
|
Aydin, Mustafa |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
59 |
| Issue:
|
5 |
| Year:
|
2023 |
| Pages:
|
411-420 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, we find all integer solutions $ (x, y, n, a, b, c) $ of the equation in the title for non-negative integers $ a, b$ and $ c $ under the condition that the integers $ x $ and $ y $ are relatively prime and $ n \ge 3$. The proof depends on the famous primitive divisor theorem due to Bilu, Hanrot and Voutier and the computational techniques on some elliptic curves. (English) |
| Keyword:
|
diophantine equations |
| Keyword:
|
primitive divisor theorem |
| Keyword:
|
Ramanujan-Nagell equations |
| MSC:
|
11D59 |
| MSC:
|
11D61 |
| MSC:
|
11Y50 |
| idZBL:
|
Zbl 07790556 |
| idMR:
|
MR4641955 |
| DOI:
|
10.5817/AM2023-5-411 |
| . |
| Date available:
|
2023-08-15T13:39:51Z |
| Last updated:
|
2024-02-13 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/151797 |
| . |
| Reference:
|
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| Reference:
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