请问一个 prime factor 的问题？

cooperqi

正的偶整数n, 函数f(n)定义成所有from 2 to n 的正的偶整数的乘积， 那f(100)+1的最小的prime factor是什么：

a. bwteen 2 and 10

b. between 10 and 20

c. between 20 and 30

d. between 30 and 40

e. >40

是prep上的，头大，搞不出。

谢谢了。

lixinli

这个题从TESTMAGIC上找到解法

f(100)=(2^50)*(50!)+1

Note that product has as factors all numbers from 1 to 50 so h(100)+1 will NOT be divisible by any of those since the remainder would be 1. So smallest prime factor has got to be more than 50. Answer is E.

cooperqi

thank you.