[求助]prep-ps1-7

ziwingfong

请教一道ｐｒｅｐ题，完全没有头绪。今天开始作数学ｐｒｅｐ，太受打击了。

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

ziwingfong

thanks  a  lot !!!!

peiyangzhe

1、H(100)+1=2*4*6.....*100=2^50*(1*2*3*4*5..........*50)+1

p是H(100)+1的最小质因子，p不可能有1，2，3.....50的因子。

M和M+1是互质的，比如24和25，26和27等等，双方不可能含有对方的除了1以外的因子。