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

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.

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！

kevin_8p

楼上的。

这里有一个性质。

任何两个连续整数是互质的。

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

lzgzszcas

明白了，多谢解答