Geodesic
On a divisibility problem
Mathematica Bohemica, Tome 144 (2019) no. 2, pp. 125-135.

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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.
DOI : 10.21136/MB.2018.0058-17
Classification : 11A25, 11B83
Keywords: prime; divisibility; exponent; Sándor-Luca's theorem 
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Yang, Shichun; Luca, Florian; Togbé, Alain. On a divisibility problem. Mathematica Bohemica, Tome 144 (2019) no. 2, pp. 125-135. doi : 10.21136/MB.2018.0058-17. http://geodesic.mathdoc.fr/articles/10.21136/MB.2018.0058-17/

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