求助PREP的数学题！！

sss000 · 发表于 2011-6-23 21:53:38

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 isA. between 2 and 10
B. between 10 and 20
C. between 20 and 30
D. between 30 and 40
E. greater than 40

请问为什么选择是E啊？？smallest prime factor应该有2的啊?
多谢！！

chelseeea · 发表于 2011-6-23 22:07:46

n=2k

h(n)=2*4*6*...*2k=(1*2)*(2*2)*(3*2)*...*(k*2)
=(2^k)*k!

n=100
k=50
h(100)+1=(2^50)*50!+1

在50之前除所有数都是余1

最小PRIME必须大于50

sss000 · 发表于 2011-6-23 22:41:26

多谢

求助PREP的数学题！！

所属分类: GMAT考试

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