今天做prep遇到一道超难的数学题，真心是不会啊！求大牛帮忙

Cambridgen · 发表于 2013-4-30 17:58:50

For every positive even integer n, the functionh(n) is defined to be the product ofall even integers from 2 to n, inclusive. If p is the smallest prime factor of h(100)+1,the p is :

Between 2 to 10

Between 10 to 20

Between 20 to 30

Between 30to 40

Greater than 40

正确答案是最后一个>40
求指教！

zongziphoto · 发表于 2013-5-4 14:36:30

f(100)+1= (2 x 1) x (2 x 2) x (2 x 3) x ... x (2 x 50)+1
=2 x (1 x 2 x 3 x ... x 50) + 1
所以1到50的所有整数都不是它的因子因为总有余数1
因此f(100)+1不可能有小于或等于50的因子更加没有质因子所以 the smallest prime number that can be a factor of h(100) + 1 has to be greater than 50
根据选项选E

Cambridgen · 发表于 2013-5-4 15:40:36

zongziphoto 发表于 2013-5-4 14:36
f(100)+1= (2 x 1) x (2 x 2) x (2 x 3) x ... x (2 x 50)+1
=2 x (1 x 2 x 3 x ... x 50) + ...

谢啦，虽然我之前已经搞明白了

今天做prep遇到一道超难的数学题，真心是不会啊！求大牛帮忙

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