大家帮忙看看啊，一道prep题

GreenHorse

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

shelleyzhdai

h(100)=2*4*6*....*100=2^50*(1*2*3*4*5...*50)，所以h(100)能够被1－50的数除，而h(100)和h(100)+1是连续的整数，所以互质，所以h(100)+1的最小质因子大于50，所以选E

xiaoqinqin

答案是E

h(100)+1=2x4x6x8....x100=2^50*50!+1

50!可以被50以内的任何一个正整数整除，h(100)+1被1-50任何一个整除后余1

所以没有小于50的质因子

GreenHorse

原来是这样...  thanks !!!!!!