prep数学一题 求指导！~~~

djsapple

prep中有一道题是这样的：
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(n)+1, then p is?
a. less than 10
b. 10 to 20
c. 20 to 30
d. 30 to 40
e. greater than 40
当时乱选了一个大于40，就对了，谁能详细讲解一下呢~ 谢啦

arleneyau

好多帖子都讨论过这题。。因为h(100)=2*4*6*8……*100=2^50*50!
所以1~50被h(100)+1除之后都会余1，所以它最小的factor必须大于50

亮亮dmx123

谢谢！

sonicwolf

疑惑，比如N=4
h(n)+1=2*4+1=9 Prime factor=3
N=8
h(n)+1=2*4*6*8+1=385 Prime factor=5