求助！prep模考里的1道题，希望nn帮助！

vivian_dong

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

prep模考里的1道题，希望nn帮助！

zacharyzhang

h(100)=2^50*(1*2*3*...*50),是1~50的整倍数。

h(100)+1除1~50的任何数都余1,因此如果h(100)+1有质因数，绝不在1~50中。也就是说最小的质因数要超过50。

vivian_dong

谢谢大n指点！