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Keywords:
prime; divisibility; exponent; Sándor-Luca's theorem
prime; divisibility; exponent; Sándor-Luca's theorem
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.
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