| Title:
|
On a divisibility problem (English) |
| Author:
|
Yang, Shichun |
| Author:
|
Luca, Florian |
| Author:
|
Togbé, Alain |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
144 |
| Issue:
|
2 |
| Year:
|
2019 |
| Pages:
|
125-135 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $p_{1}, p_{2}, \cdots $ be the sequence of all primes in ascending order. Using explicit estimates from the prime number theory, we show that if $ k \geq 5 $, then $$ (p_{k+1}-1)! \mid (\tfrac {1}{2} (p_{k +1} - 1))! p_ {k}!, $$ which improves a previous result of the second author. (English) |
| Keyword:
|
prime |
| Keyword:
|
divisibility |
| Keyword:
|
exponent |
| Keyword:
|
Sándor-Luca's theorem |
| MSC:
|
11A25 |
| MSC:
|
11B83 |
| idZBL:
|
Zbl 07088840 |
| idMR:
|
MR3974182 |
| DOI:
|
10.21136/MB.2018.0058-17 |
| . |
| Date available:
|
2019-06-21T11:31:57Z |
| Last updated:
|
2020-07-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147754 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| . |
