Prep Math Difficult question

springhot · 发表于 2010-8-19 11:27:21

For every positive even integer n, the funtion h(n) is defined to be the product of all 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....
c...
d...
e: greater than 40
The answer is e. How do we get the answer?

promiselu · 发表于 2010-8-19 15:55:28

【答案】E
【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

Prep Math Difficult question

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