各路大神帮解一道数学题吧~~~

yiliacao · 发表于 2012-10-24 16:28:17

prep上遇到的
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

HerringtonD · 发表于 2012-10-24 16:38:34

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

thus 1-50 are all factors of h(100). 1~50 cannot be the factor of h(100)+1 since h(100)+1 cannot be divided by 1~50 without remainder.

so, the answer is E

yiliacao · 发表于 2012-10-24 16:52:16

感谢大神！

各路大神帮解一道数学题吧~~~

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