prep07的一道数学题

卡霍

上了大学后，我就成文科生了。这年头，连数学都做不好了，唉。。。
请教各位N一道题，
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
A. between 2 and 10

卡霍

不好意思，发错了。。。

卡霍

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

aaroncheng

选 E
h(100)+1= 2^50×50！＋1  
由上可知： 50以内都不会有它的factor，因为有50！和1的存在

卡霍

是的，可是怎么算的呀。。。我一碰上这种大数字就头疼啊。。。

aaroncheng

上面给你回复了，就是因为有1那个余数的存在，50以内只要能被h（100）整除的都不能被h（100）+1 整除

卡霍

明白了。。。O(∩_∩)O谢谢
我一看到这种大数字就头疼