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 the smallest prime factor of h(100) +1 , then p is ？
答案：greater than 40作者: arthurman 时间: 2011-5-11 06:36
This one has been explained before.
Basically,
1) These consecutive natural numbers h(100) and [h(100) + 1] are co-prime, meaning that they do not share any prime numbers as their cofactors.
2) h(100) contains all the prime numbers between 2 (from 2) and 47 (from 94).
3) Then prime numbers among factors of [h(100) + 1] would not include any prime numbers between 2 and 47.
4) Then the smallest prime facotr of [h(100) + 1] is bigger than 47.作者: boystar 时间: 2011-5-11 21:07
明白啦，谢谢楼上!作者: eeheaven 时间: 2011-5-12 06:40
请问，这个47是怎么来的啊？作者: arthurman 时间: 2011-5-13 06:43
94 = 2*47. So 47 is a factor of h(100).
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