求一道prep 数学题解答

predx · 发表于 2013-6-19 21:11:20

For every positive even integer n, the function h(n) is defined to be the product of all the even integers from 2 ton, 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

答案选E ，想不通，请大牛们帮忙解释一下

francoisyang · 发表于 2013-6-20 09:46:20

h(100)+1=2*4*8*......*100+1=2^a*3^b*5^c*....*47+1
h(100)的质因数包含2到47之内的所有质数，所以h(100)+1不可能有低于47的质因数。

predx · 发表于 2013-6-23 18:29:03

弱弱地问一下：2^a*3^b*5^c*....*47+1 是什么意思，为啥h(100)+1 就不可能有低于47的质数？求解释

求一道prep 数学题解答

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