| Title:
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On repdigits as product of $k$-Fibonacci and $k$-Lucas numbers (English) |
| Author:
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Seffah, Safia |
| Author:
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Rihane, Salah Eddine |
| Author:
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Togbé, Alain |
| Language:
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English |
| Journal:
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Mathematica Bohemica |
| ISSN:
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0011-4642 |
| ISSN:
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0862-7959 (print) |
| ISSN:
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2464-7136 (online) |
| Volume:
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151 |
| Issue:
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1 |
| Year:
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2026 |
| Pages:
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29-55 |
| Summary lang:
|
English |
| . |
| Category:
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math |
| . |
| Summary:
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For an integer $k\geq 2$, let $(F_{n}^{(k)})_{n\geq -(k-2)}$, $(L_{n}^{(k)})_{n \geq -(k-2)}$ be $k$-Fibonacci and $k$-Lucas sequences, respectively. For these sequences the first $k$ terms are $0,\ldots ,0,1$ and $0,\ldots ,0,2,1$, respectively, and each term afterwards is the sum of the preceding $k$ terms. In this paper, we determine all possibilities such that $F_{n}^{(k)} L_{m}^{(k)}$ can represent a repdigit. (English) |
| Keyword:
|
$k$-Fibonacci numbers |
| Keyword:
|
$k$-Lucas numbers |
| Keyword:
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repdigits |
| Keyword:
|
linear form in logarithms |
| Keyword:
|
reduction method |
| MSC:
|
11B39 |
| MSC:
|
11J86 |
| DOI:
|
10.21136/MB.2025.0035-24 |
| . |
| Date available:
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2026-02-19T13:51:45Z |
| Last updated:
|
2026-02-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/153385 |
| . |
| Reference:
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