prep上一道题求解

sophiagregmat · 发表于 2012-7-29 14:03:12

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
求解，谢谢！

玖月SEP · 发表于 2012-7-29 15:25:19

【思路】
假設h(100)+1最小因數是 n , n<50 例如47好了, 既然47是因數, 他就能整除h(100)+1 可是發現h(100)裡面有47的因數,可以整除那h(100)+1被47除的餘數為1,表示47不是h(100)+1的因數同理去想小於50的其它因式也是會一樣的結果所以h(100)+1的因式是在大於50外
重點在那50!, 假如小於50的質數是h(100)的factor,那就不會是h(100)+1的factor ,因為餘數會是1

sophiagregmat · 发表于 2012-7-29 21:23:04

谢谢解答~~~

prep上一道题求解

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