请教一道prep题。。关于质因子的

painstak

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 factorof h(100)+1, the p is

A. between 2 and 10

B. between 10 and 20

C. between 20 and 30

D. between 20 to 40

E. greater than 40

请nn们不吝赐教。。。多谢

lzgzszcas

明白了，多谢解答

xiayizhang

tat is to say h(100) has 1~50 as factors. h(100)+1 will have prime factors other than those prime factors inside 1~50

kevin_8p

楼上的。

这里有一个性质。

任何两个连续整数是互质的。

lzgzszcas

就算看了解释，还是没看明白，P是H(100)+1最小的质因子，

“that is to say, h(100) + 1 cannot have any prime factors 50 or below.”
为什么H（100）的因子包括所有的50以下的质数，就能得出上面的结论？
请大家指教，多谢！

taoyeye

h(100) = 2*4*6*8*...*100
By factoring a 2 from each term, h(100) can be rewritten as
2^50*(1*2*3*...*50).

Thus, all integers up to 50 - including all prime numbers up to 50 - are factors of h(100).

that is to say, h(100) + 1 cannot have any prime factors 50 or below.