[求助]一道PREP数学题

huangxiaoyan

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 (answer :greater than 40)

阿本

跟据h(n)的定义

h(100)=2*4*6*......*100=(2^50)*(1*2*3*......*50)=(2^50)*50!

所以h(100)+1被50以内的所有整数除的时候，余数都为1，也就是说不能被50以内的所有整数整除

因此h(100)+1的最小质因子一定大于50

huangxiaoyan

多谢