请教一题数学题~急求！！

q101018013

For every positive even interger n, the function h (n) is defined to be the product of all the even integers from 2 to n.If p is the smallest prime factor of h(100)+1, then p is

between 2 and 10
             10        20
greater than 40

answer is greater than 40.
求问怎么知道是大于40？？

xiangyu4255

根据题目:

h (100)=2x4x6...x100=2^50x1x2x3...50

所以这个 h (100)可以是2-50内任意一个数的整数倍，也就说 h (100)能被2-50内任意一个整数整除。那么 h (100)+1就不能被任意一个2-50内任意一个整数整除，所以 h (100)+1的最小质因子一定是大于50的数，具体是多少就不用管了，说不定它就是个质数呢

lisney

顶顶顶！纠结了半天终于懂啦