一个包含F.Smarandache LCM函数的猜想

A Conjecture Involving the F.Smarandache LCM Function

对任意正整数n,著名的F.Smarandache LCM函数SL(n)定义为最小的正整数k,使得n|[1,2…,k],这里[1,2…,k]表示1,2…,k的最小公倍数.本文利用初等方法研究张文鹏在他所著的《初等数论》一书中提出的一个包含F.Smarandache LCM函数的猜想,并有了实质性进展.

For any positive integer n, the famous F.Smarandache LCM Iunction SL（n） is defined as the smallest positive integer k such that nI [1, 2,..., k], where [1, 2,..., k] denotes the least common multiple of 1, 2 k. The main purpose of this paper is to use using the elementary methods to study a conjecture involving the F.Smarandache LCM function, which is proposed by Zhang Wenpeng in his book ＂Elementary Number Theory＂, thus making some substantial progress for this conjecture.