For every positive even integer n, the function h(n) is defined to be the product of all the even integers from 2 to n, inclusive.  If p is the smallest prime factor of h(100) + 1, then p is

(A) between 2 and 10

(A) between 2 and 10

(A) between 2 and 10

(B) between 10 and 20

(C) between 20 and 30

(D) between 30 and 40

(E) greater than 40

不会做呢。求助！谢谢了！

是这样的：

h(100) = 2*4*6*8*...*100

h(100) = 2^50*(1*2*3*...*50)
而两个连续自然数的质因子是完全不同的（可验证），所以h(n)+1和h(n）的质因子肯定不一样。而h也就是说50以下的数都是h(100)的因子，即h(100)+1的质因子都大于50。

不过算出来greater than 50

这时候选E greater than 40

为何可以选E 还是因为只有这选项最接近 就选呢

两个连续自然数的质因子是完全不同的（可验证）

老美的数学有这么厉害呀? 我都不知道这个定理