问一道数学题

ph.shout911

问一道数学题，实在不会做：

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 to 10;
B. between 10 to 20;
C. between 20 to 30;
D. between 30 to 40;
E. greater than 40.

答案是E, 不知道为什么？

当你年老

P要大于50 如果P不大于50 比如是47 h（100)这部分是可以整除它的 因为其中包含了47*2=94 所以会余1

徜徉梦境

h(100)+1=2*4*6*……*100+1,即h(100)+1=2*(1*2*3*……*50）+1=2*50！+1，所以h(100)+1除以1到50的每个数都会余1，所以最小的质数一定＞50

ph.shout911

我明白了，谢谢大家。