超级难题求解 - Prep-PS1-7

dove_hp

7.    905-!-item-!-187;#058&000575

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 and 10

(A) between 2 and 10

(B) between 10 and 20

(C) between 20 and 30

(D) between 30 and 40

(E) greater than 40

不会做呢。求助！谢谢了！

[此贴子已经被作者于2008-8-12 12:02:35编辑过]

ada3063

http://forum.chasedream.com/dispbbs.asp?BoardID=22&ID=150738

dove_hp

Thank you Ada!

dove_hp

喔，原来是这样的：

h(100) = 2*4*6*8*...*100 

h(100) = 2^50*(1*2*3*...*50)
而两个连续自然数的质因子是完全不同的（可验证），所以h(n)+1和h(n）的质因子肯定不一样。而h也就是说50以下的数都是h(100)的因子，即h(100)+1的质因子都大于50。

william0625

不过算出来greater than 50

这时候选E greater than 40

为何可以选E 还是因为只有这选项最接近 就选呢

william0625

顶

请nn帮忙

卖菜熊

我不是NN。。。我想说你有点钻牛角尖了吧，这里5个选项，不选大于40还选哪个啊。。。