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[求助]关于问题求解,不太理解答案何来……

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楼主
发表于 2008-7-25 11:45:00 | 只看该作者

[求助]关于问题求解,不太理解答案何来……

For every positive enen interger n, the function h(n) is defined to be the product of all the even ingergers from 2 to n, inclusive. If P is the smallesting prime factor of h(100)+1 ,then p is ____


答案: more than 40



In a certain bathbub, both the cold water and the hot water fixtures leak. The clod-water would fill an empty bucket in c hours and the hot water leak alone would fill the same bucket in h hours where c<h, If both fixtures began to leak at the rates and consequently it took t hours to fill the bucket, which of the following must be true?


1. 0<t<h


2. c<th


3. c/2<t<h/2


答案:1&3

哪位nn能解释一下why么?

沙发
 楼主| 发表于 2008-7-25 14:53:00 | 只看该作者

已经琢磨出第二天如何解,但是第一题就……

毛人offer help么?

板凳
发表于 2008-7-25 15:41:00 | 只看该作者
Question has been asked many times just in these 2 days.

h(100) = 2*4*...*100 = 2^50*50! Since 50! is divisible by any number from 1 to 50, the smallest prime factor of 2^50*50!+1 can only be greater than 50. Any number less than 50 (including all the prime numbers less than 50) will result in a remainder of 1.

[此贴子已经被作者于2008-7-25 15:44:44编辑过]
地板
 楼主| 发表于 2008-7-28 11:39:00 | 只看该作者
谢谢ls的解答~
5#
发表于 2008-7-28 14:42:00 | 只看该作者
能解释一下第二题里面的3. 怎么成立的吗?
6#
发表于 2008-7-28 14:57:00 | 只看该作者
以下是引用ledazhou在2008-7-28 14:42:00的发言:
能解释一下第二题里面的3. 怎么成立的吗?

t=1/(1/c+1/h)=ch/c+h

代入到c/2<t<h/2里面去验算一下就可以了。

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