求教大家一道数学题，真的不懂~

sandychen168 · 发表于 2010-10-20 19:09:27

题目在这里：
For every positive even integer n,the function h(n) is defined to be the product of all the even integer from 2 to n,inclusive.If p is the smallest prime factor of h(100)+1,then p is

求教大家，真的不会做~

buffonjuventus · 发表于 2010-10-20 19:10:39

看不到你的题目……

xiaoguolulu · 发表于 2010-10-20 19:12:32

囧···看不到题目，还是别截图，直接打字吧

tlmoonsand · 发表于 2010-10-20 19:24:06

恩同看不到题目~

sandychen168 · 发表于 2010-10-20 20:11:26

重新发了题目，请大家指教~

澹泓幽客 · 发表于 2010-10-20 20:16:10

h（100）=2*4*。。。*100
最大的质因数应该是47
所以H（100）+1最小的质因数应该至少大于47.
我是这么觉得的。

sandychen168 · 发表于 2010-10-20 20:25:08

能说明下原因吗？

midforest · 发表于 2010-10-20 20:57:14

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.

sandychen168 · 发表于 2010-10-20 22:23:11

thank you very much，i got it~~~

sandychen168 · 发表于 2010-10-20 22:30:09

Thank you very much,it is clear and precise.I totally got it~

求教大家一道数学题，真的不懂~

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