| Title:
|
Complete solutions of a Lebesgue-Ramanujan-Nagell type equation (English) |
| Author:
|
Baruah, Priyanka |
| Author:
|
Das, Anup |
| Author:
|
Hoque, Azizul |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
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0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
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60 |
| Issue:
|
3 |
| Year:
|
2024 |
| Pages:
|
135-144 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We consider the Lebesgue-Ramanujan-Nagell type equation $x^2+5^a13^b17^c=2^m y^n$, where $a,b,c, m\ge 0, n \ge 3$ and $x, y\ge 1$ are unknown integers with $\gcd (x,y)=1$. We determine all integer solutions to the above equation. The proof depends on the classical results of Bilu, Hanrot and Voutier on primitive divisors in Lehmer sequences, and finding all $S$-integral points on a class of elliptic curves. (English) |
| Keyword:
|
Diophantine equation |
| Keyword:
|
Lehmer sequence |
| Keyword:
|
elliptic curve |
| Keyword:
|
quartic curve |
| Keyword:
|
S-integral points |
| MSC:
|
11D41 |
| MSC:
|
11D61 |
| MSC:
|
11Y50 |
| DOI:
|
10.5817/AM2024-3-135 |
| . |
| Date available:
|
2024-08-02T08:32:57Z |
| Last updated:
|
2024-08-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/152521 |
| . |
| Reference:
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