prep h(n)的最小质因素那题

7.    905-!-item-!-187;#058&000575

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

(B) between 10 and 20

(C) between 20 and 30

(D) between 30 and 40

(E) greater than 40

E

求思路，只知h(n)=2*50!+1

等一下,h(n)=2*50!+1 吗???

我怎么觉得应该是h(n)=2⁵⁰×50!+1 呢?????

crowkiller 说的"h(n) 不能被 1-50中任意一个数整除"挺有道理的

m= 2k+1, m 不能被2整除，p=3k+1,p不能被3整除，

==>h(n)=2*50!+1   ==> h(n) 不能被 1-50中任意一个数整除

==》E

有理

当时模考就是大概这样猜到答案，看来没有其他确定的推理，就按这样的规律了。

谢谢。