On a divisibility problem

Shichun Yang; Florian Luca; Alain Togbé

Mathematica Bohemica (2019)

  • Volume: 144, Issue: 2, page 125-135
  • ISSN: 0862-7959

Abstract

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Let p 1 , p 2 , ⋯ be the sequence of all primes in ascending order. Using explicit estimates from the prime number theory, we show that if k ≥ 5 , then ( p k + 1 - 1 ) ! ∣ ( 1 2 ( p k + 1 - 1 ) ) ! p k ! , which improves a previous result of the second author.

How to cite

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Yang, Shichun, Luca, Florian, and Togbé, Alain. "On a divisibility problem." Mathematica Bohemica 144.2 (2019): 125-135. <http://eudml.org/doc/294176>.

@article{Yang2019,
abstract = {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 \ge 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.},
author = {Yang, Shichun, Luca, Florian, Togbé, Alain},
journal = {Mathematica Bohemica},
keywords = {prime; divisibility; exponent; Sándor-Luca's theorem},
language = {eng},
number = {2},
pages = {125-135},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On a divisibility problem},
url = {http://eudml.org/doc/294176},
volume = {144},
year = {2019},
}

TY - JOUR
AU - Yang, Shichun
AU - Luca, Florian
AU - Togbé, Alain
TI - On a divisibility problem
JO - Mathematica Bohemica
PY - 2019
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 144
IS - 2
SP - 125
EP - 135
AB - 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 \ge 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.
LA - eng
KW - prime; divisibility; exponent; Sándor-Luca's theorem
UR - http://eudml.org/doc/294176
ER -

References

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