| Title:
|
Bartz-Marlewski equation with generalized Lucas components (English) |
| Author:
|
Hashim, Hayder R. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
58 |
| Issue:
|
3 |
| Year:
|
2022 |
| Pages:
|
189-197 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $\lbrace U_n\rbrace =\lbrace U_n(P,Q)\rbrace $ and $\lbrace V_n\rbrace =\lbrace V_n(P,Q)\rbrace $ be the Lucas sequences of the first and second kind respectively at the parameters $P \ge 1$ and $Q \in \lbrace -1, 1\rbrace $. In this paper, we provide a technique for characterizing the solutions of the so-called Bartz-Marlewski equation \[ x^2-3xy+y^2+x=0\,, \] where $(x,y)=(U_i, U_j)$ or $(V_i, V_j)$ with $i$, $ j \ge 1$. Then, the procedure of this technique is applied to completely resolve this equation with certain values of such parameters. (English) |
| Keyword:
|
Lucas sequences |
| Keyword:
|
Diophantine equation |
| MSC:
|
11B39 |
| MSC:
|
11D45 |
| idZBL:
|
Zbl 07584090 |
| idMR:
|
MR4483053 |
| DOI:
|
10.5817/AM2022-3-189 |
| . |
| Date available:
|
2022-09-01T10:21:56Z |
| Last updated:
|
2023-03-13 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/150664 |
| . |
| 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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| . |
