1，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
1) between 2 and 10
2)between 10 and 20
3)between 20 and 30
4)between 30 and 40
5)greater than 40
Answer is 5)greater than 40作者: reddragon 时间: 2010-12-21 19:56
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: songxuebest 时间: 2010-12-22 20:46
Hey thank you so much! I got it right now. Really appreciate your answer.作者: georgina1107 时间: 2010-12-23 20:02
2) h(100) contains all the prime numbers between 2 (from 2) and 47 (from 94).
So the product of the second series contains factors of 2 and 2, 3, 4 ,5, 6, 7, 8, 9, . . . 46, 47, 48, 49, 50.
47 is the biggest factor of h(100), which is a prime number.
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