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标题: 求助一道prep的数学题，最怕这种题了 [打印本页]

作者: scientist 时间: 2010-1-29 21:14
标题: 求助一道prep的数学题，最怕这种题了
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
(B) between 10 and 20
(C) between 20 and 30
(D) between 30 and 40
(E) greater than 40

作者: cming 时间: 2010-1-29 22:35
选e?

作者: cming 时间: 2010-1-29 22:39
给你一个google来的解题过程，

h(100)= 2*4*6............100
h(100)+1=2*4*6............100 +1
2(1*2*3.......50)+1

so when h(100)+1 is divided by any of the nos between 2 and 50 will leave a remainder 1.

2*50!+1 will not be divisible by any no <50

answer E

作者: scientist 时间: 2010-1-29 23:05
对，选e，我再仔细看看的
谢拉

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