求PREP-PS-1-7 解

jesuisdesole

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

真是没思路干瞪眼。。。。

benzine

h(100)和h(100)+1是连续的两个整数，而连续的两个整数互质，所以最大公约数为1，因此h(100)的因子不可能是h(100)+1的因子，而

h(100)=（2*1）*（2*2）*（2*3）……（2*50）=2^50*50!，故h（100）中含有1到50的所有质数，所以h（100）+1里就不可能含这些质数。

所以选E