| Title:
|
On some Diophantine equations involving balancing numbers (English) |
| Author:
|
Tchammou, Euloge |
| Author:
|
Togbé, Alain |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
57 |
| Issue:
|
2 |
| Year:
|
2021 |
| Pages:
|
113-130 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, we find all the solutions of the Diophantine equation $B_1^p+2B_2^p+\cdots +kB_k^p=B_n^q$ in positive integer variables $(k, n)$, where $B_i$ is the $i^{th}$ balancing number if the exponents $p$, $ q$ are included in the set $\lbrace 1,2\rbrace $. (English) |
| Keyword:
|
balancing numbers |
| Keyword:
|
Pell numbers |
| Keyword:
|
Diophantine equation |
| MSC:
|
11B39 |
| idZBL:
|
Zbl 07361069 |
| idMR:
|
MR4306172 |
| DOI:
|
10.5817/AM2021-2-113 |
| . |
| Date available:
|
2021-05-11T14:26:51Z |
| Last updated:
|
2021-11-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148894 |
| . |
| 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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| 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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| . |
