| Title:
|
Repdigits in the base $b$ as sums of four balancing numbers (English) |
| Author:
|
Keskin, Refik |
| Author:
|
Erduvan, Fatih |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
146 |
| Issue:
|
1 |
| Year:
|
2021 |
| Pages:
|
55-68 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The sequence of balancing numbers $(B_{n})$ is defined by the recurrence relation $B_{n}=6B_{n-1}-B_{n-2}$ for $n\geq 2$ with initial conditions $B_{0}=0$ and $B_{1}=1.$ $B_{n}$ is called the $n$th balancing number. In this paper, we find all repdigits in the base $b,$ which are sums of four balancing numbers. As a result of our theorem, we state that if $B_{n}$ is repdigit in the base $b$ and has at least two digits, then $(n,b)=(2,5),(3,6) $. Namely, $B_{2}=6=(11)_{5}$ and $B_{3}=35=(55)_{6}.$ (English) |
| Keyword:
|
balancing number |
| Keyword:
|
repdigit |
| Keyword:
|
Diophantine equations |
| Keyword:
|
linear form in logarithms |
| MSC:
|
11B39 |
| MSC:
|
11D61 |
| MSC:
|
11J86 |
| idZBL:
|
07332742 |
| idMR:
|
MR4227311 |
| DOI:
|
10.21136/MB.2020.0077-19 |
| . |
| Date available:
|
2021-03-12T16:19:39Z |
| Last updated:
|
2021-04-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148747 |
| . |
| 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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| . |
