请教ppt 一道数学题

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

(1) between 2 and 10

(2) between 10 and 20

(3) between 20 and 30

(4) between 30 and 40

(5) greater than 40

是(5)吗?

h(100)+1=2X4X6X8X......X98X100+1=1X2X3X.....X49X50X(2的50次方)+1

则h(100)+1除以任何小于50的数都会余1,也就是h(100)+1不会被任何小于50的数整除,当然也包括任何小于40的质数.

因此最小的质因子肯定是大于40的

答案就是(5).

终于明白了,多谢.

You are welcome