Mathematica Bohemica, Vol. 144, No. 2, pp. 125-135, 2019


On a divisibility problem

Shichun Yang, Florian Luca, Alain Togbé

Received June 8, 2017.   Published online June 5, 2018.

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 \geq5 $, then $(p_{k+1}-1)! \mid(\tfrac12 (p_{k +1} - 1))! p_ k!$, which improves a previous result of the second author.
Keywords:  prime; divisibility; exponent; Sándor-Luca's theorem
Classification MSC:  11A25, 11B83


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Affiliations:   Shichun Yang, College of Mathematics and Computer Science, Institute of Mathematics, ABa Teachers University, Sichuan 623000, P. R. China, e-mail: ysc1020@sina.com; Florian Luca, School of Mathematics, University of the Witwatersrand, Private Bag X3, Wits 2050, South Africa and Department of Mathematics, Faculty of Sciences, University of Ostrava, 30. dubna 22, 701 03 Ostrava 1, Czech Republic, e-mail: florian.luca@wits.ac.za; Alain Togbé, Department of Mathematics, Statistics and Computer Science, Purdue University Northwest, 1401 S, U.S. 421, Westville IN 46391 USA, e-mail: atogbe@pnw.edu


 
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