请教NN一道想了好几天的数学题

insonbia83

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

请教NN们  这题怎么算啊？？？ 谢谢！！

xiaoxiugirl

提示你一下

你把2提出来 就变成2^50*(1*2*3......*50)+1

会了没?

BruceNornia

h(100) + 1 = 2*4*6*...*98*100 +1

= 2^50 * (1*2*3*...*49*50) + 1

 

从上面这个式子可以看出 对于所有小于等于50 大于等于2 的正整数， h(100) +1 都是不能被整除的 即这些数均不可能是它的因数

所以h(100) + 1 的最小的质因数一定大于50

E