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排列组合是高中数学的一个重要内容,同时也是高考和数学竞赛中的热点,其重要性不言而喻,而利用排列组合可以解决许多数学问题。本文将给出排列组合公式在初等数论中的一个应用——解决关于D(n)的上界估计问题。设m=p_1p_2…p_n,其中p_i(i=1,2,…,n)是不同的素数,D(n)表示m的所有不同乘积的个数,显然这个数只与素数的个数n有关,而与那些具体素数无关。关于D(n)的上界估计和精确公式至今没有解决。本文将利用排列组合知识给出有关D(n)的上界估计
Permutations and combinations are an important part of high school mathematics. They are also hot topics in college entrance examination and mathematics contests. Their importance is self-evident. Using permutations and combinations can solve many mathematical problems. In this paper, we present an application of permutation and combination formulas in elementary number theory - solving the upper bound of D (n). Let m = p_1p_2 ... p_n, where p_i (i = 1,2, ..., n) is a different prime and D (n) is the number of all the different products of m. Obviously, this number is only related to the number n of primes , But not with those specific primes. The upper bound estimation and exact formula for D (n) have not been solved yet. This article will use the permutation and combination knowledge to give the upper bound estimate of D (n)