Commun. Korean Math. Soc. 2002 Vol. 17, No. 3, 541-550 Printed September 1, 2002

Youngmee Koh, Sangwook Ree The University of Suwon, The University of Suwon

Abstract : In this paper, we look at a simple function $L$ assigning to an integer $n$ the smallest positive integer $m$ such that any product of $m$ consecutive numbers is divisible by $n$. Investigated are the interesting properties of the function. The function $L(n)$ is completely determined by $L(p^k)$, where $p^k$ is a factor of $n$, and satisfies $L(m \cdot n) \leq L(m)+L(n)$, where the equality holds for infinitely many cases.

Keywords : divisors of the products of consecutive integers