请教prep数学题

whsirius · 发表于 2011-4-10 11:14:19

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

sdcar2010 · 发表于 2011-4-10 12:54:20

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.

whsirius · 发表于 2011-4-10 13:03:57

明白啦，谢谢楼上的美女NN~~

charlenechase · 发表于 2011-4-26 15:51:36

请问，这个47是怎么来的啊？

sdcar2010 · 发表于 2011-4-26 20:50:54

94 = 2*47. So 47 is a factor of h(100).

请教prep数学题

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