| Title:
|
The method of infinite ascent applied on $A^4 \pm n B^3 = C^2$ (English) |
| Author:
|
Jena, Susil Kumar |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
63 |
| Issue:
|
2 |
| Year:
|
2013 |
| Pages:
|
369-374 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Each of the Diophantine equations $A^4 \pm nB^3 = C^2$ has an infinite number of integral solutions $(A, B, C)$ for any positive integer $n$. In this paper, we will show how the method of infinite ascent could be applied to generate these solutions. We will investigate the conditions when $A$, $B$ and $C$ are pair-wise co-prime. As a side result of this investigation, we will show a method of generating an infinite number of co-prime integral solutions $(A, B, C)$ of the Diophantine equation $aA^3 + cB^3 = C^2$ for any co-prime integer pair $(a,c)$. (English) |
| Keyword:
|
method of infinite ascent |
| Keyword:
|
Diophantine equation $A^4 \pm nB^3 = C^2$ |
| MSC:
|
11D41 |
| MSC:
|
11D72 |
| idZBL:
|
Zbl 06236416 |
| idMR:
|
MR3073963 |
| DOI:
|
10.1007/s10587-013-0022-4 |
| . |
| Date available:
|
2013-07-18T14:51:37Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143317 |
| . |
| Reference:
|
[1] Beukers, F.: The Diophantine equation $Ax^p + By^q = Cz^r$.Duke Math. J. 91 (1998), 61-88. MR 1487980, 10.1215/S0012-7094-98-09105-0 |
| Reference:
|
[2] Jena, S. K.: Method of infinite ascent applied on $A^4 \pm nB^2 = C^3$.Math. Stud. 78 (2009), 233-238. MR 2779731 |
| Reference:
|
[3] Jena, S. K.: Method of infinite ascent applied on $mA^3 + nB^3 = C^2$.Math. Stud. 79 (2010), 187-192. MR 2906833 |
| . |
