PRPE一道数学PS题，看了破解还是不会

花花的世界 · 发表于 2010-8-23 18:40:50

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

(A) between 2 and 10

(B) between 10 and 20

(C) between 20 and 30

(D) between 30 and 40

(E) greater than 40

答案是E...
请问这个答案是如何而来的啊？？谢谢~~

wenjie87 · 发表于 2010-8-23 18:48:55

帮你顶一下，我也没看明白

nioni · 发表于 2010-8-23 19:33:14

那个应该求2*4*6*……*100+1的最小质因子吧，可是不会求
帮顶

lzczjgsu · 发表于 2010-8-23 19:51:37

这是老版的prep还是新版的破解的题？

花花的世界 · 发表于 2010-8-28 16:54:58

回楼上，新版的哈~~ 有没有人知道啊？？

uwants · 发表于 2010-8-28 17:25:04

By factoring a 2 from each term of our function, h(100) can be rewritten as
2^50*(1*2*3*...*50).

Thus, all integers up to 50 - including all prime numbers up to 50 - are factors of h(100).

Therefore, h(100) + 1 cannot have any prime factors 50 or below, since dividing this value by any of these prime numbers will yield a remainder of 1.

Since the smallest prime number that can be a factor of h(100) + 1 has to be greater than 50, The correct answer is E.

lyria · 发表于 2010-8-28 17:31:56

LS正解。简而言之就是h(100)=2*4*6*8...*100=2*2*2*2*3*2*4...*2*50所以它能被1-50的所有数整除，因此h(100)+1就不能被1-50的任何数整除了，因此最小质因子肯定大于50。（如果a能被b整除（b不是1。。），a+1就不能被b整除）

PRPE一道数学PS题，看了破解还是不会

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