| Title:
|
Fermat $k$-Fibonacci and $k$-Lucas numbers (English) |
| Author:
|
Bravo, Jhon J. |
| Author:
|
Herrera, Jose L. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
145 |
| Issue:
|
1 |
| Year:
|
2020 |
| Pages:
|
19-32 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Using the lower bound of linear forms in logarithms of Matveev and the theory of continued fractions by means of a variation of a result of Dujella and Pethő, we find all $k$-Fibonacci and $k$-Lucas numbers which are Fermat numbers. Some more general results are given. (English) |
| Keyword:
|
generalized Fibonacci number |
| Keyword:
|
Fermat number, linear form in logarithms |
| Keyword:
|
reduction method |
| MSC:
|
11B39 |
| MSC:
|
11J86 |
| idZBL:
|
07217177 |
| idMR:
|
MR4088690 |
| DOI:
|
10.21136/MB.2018.0015-18 |
| . |
| Date available:
|
2020-03-12T08:18:32Z |
| Last updated:
|
2020-11-18 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148061 |
| . |
| 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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| Reference:
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| Reference:
|
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| Reference:
|
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| Reference:
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| . |
