pp3難題，請諸位高手看看

srere

For every positive interger n, the function h(n) is defined to be 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
b. between 10 and 20
c. between 20 and 30
d. between 30 and 40
e. greater than 40

這題真是想不出來，請諸位高手解看看.....

發現PP3中還真有一些變化題型呢！

hitlzc

这题前几天有人问过，有高手给出了经典回答：

h(100)+1和h(100)是互质的，互质的两个数因子必然不同，而h(100)=(2^50)(50!)，因子为2-50，

所以P>50

ppbb

Hitlzc,

That's a smart solution.I got to remember it. Thanks.

Mine sounds more complex.

h(100)+1= 2^50 (1x 2 x 3....50)+1

a. between 2 and 10
b. between 10 and 20
c. between 20 and 30
d. between 30 and 40
If P were among these numbers, it would only satisfy "2^50 (1x 2 x 3....50)" but "1",

therefore p must be one in numbers- e. greater than 40.

hitlzc

以下是引用ppbb在2006-1-6 16:07:00的发言：

Hitlzc,

That's a smart solution.I got to remember it. Thanks.

Mine sounds more complex.

h(100)+1= 2^50 (1x 2 x 3....50)+1

a. between 2 and 10
b. between 10 and 20
c. between 20 and 30
d. between 30 and 40
If P were among these numbers, it would only satisfy "2^50 (1x 2 x 3....50)" but "1",

therefore p must be one in numbers- e. greater than 40.

哈哈，意思是一样的。这题我第一次看时也糊涂，但觉得应该选E.但说不清楚为什么，直到另外一位考友点拨，才茅塞顿开。

ppbb

I guess most of us got used to the questions in the old version of test. Plus there were lots of jj helping us. It takes a while for us to be familiar with the new ones. Anyaway, let kick GMAC's ass. Hopefully, everyone can get a desirable score!

srere

Hitlzc,ppbb

感謝感謝！解法真是神乎其技，又快又準

徹底解決小弟心中的困惑呀！

大家一起殺G吧！

tomasy

以下是引用hitlzc在2006-1-6 15:25:00的发言：

这题前几天有人问过，有高手给出了经典回答：

h(100)+1和h(100)是互质的，互质的两个数因子必然不同，而h(100)=(2^50)(50!)，因子为2-50，

所以P>50

请教, 为什么是 2 ^ 50 ?

hitlzc

以下是引用tomasy在2006-1-7 3:10:00的发言：

请教, 为什么是 2 ^ 50 ?

h(100)=2*4*6*....*100，都是偶数将2提取出来，共有50个，所以是2^50，剩下的是1*2*3...*50=50！

tomasy

以下是引用hitlzc在2006-1-7 8:10:00的发言：

h(100)=2*4*6*....*100，都是偶数将2提取出来，共有50个，所以是2^50，剩下的是1*2*3...*50=50！

谢谢 hitilzc，不好意思，再问下，什么叫互质？是互为质数．．可以解释下吗？

hitlzc

以下是引用tomasy在2006-1-7 8:41:00的发言：

谢谢 hitilzc，不好意思，再问下，什么叫互质？是互为质数．．可以解释下吗？

对对，就是除了1之外没有公因子。