On a divisibility problem

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