| Title:
|
A note on $(a,b)$-Fibonacci sequences and specially multiplicative arithmetic functions (English) |
| Author:
|
Schwab, Emil Daniel |
| Author:
|
Schwab, Gabriela |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
149 |
| Issue:
|
2 |
| Year:
|
2024 |
| Pages:
|
237-246 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A specially multiplicative arithmetic function is the Dirichlet convolution of two completely multiplicative arithmetic functions. The aim of this paper is to prove explicitly that two mathematical objects, namely $(a,b)$-Fibonacci sequences and specially multiplicative prime-independent arithmetic functions, are equivalent in the sense that each can be reconstructed from the other. Replacing one with another, the exploration space of both mathematical objects expands significantly. (English) |
| Keyword:
|
Fibonacci sequence |
| Keyword:
|
multiplicative arithmetic function |
| Keyword:
|
Binet's formula |
| Keyword:
|
Busche-Ramanujan identities |
| Keyword:
|
Möbius inversion |
| MSC:
|
11A25 |
| MSC:
|
11B39 |
| DOI:
|
10.21136/MB.2023.0102-22 |
| . |
| Date available:
|
2024-07-10T15:05:10Z |
| Last updated:
|
2024-07-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/152470 |
| . |
| Reference:
|
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| Reference:
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| . |
