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标题: gwd-26-16 [打印本页]

作者: XIAOHANMEIME 时间: 2006-8-9 06:39 标题: gwd-26-16

Q16:If n is an integer greater than 6, which of the following must be divisible by 3?

A. n (n+1) (n-4)

B. n (n+2) (n-1)

C. n (n+3) (n-5)

D. n (n+4) (n-2)

E. n (n+5) (n-6)

这个题答案A,怎么判断？

作者: dbearwangs 时间: 2006-8-9 12:51

It's easy to find that the product of any three consecutive integers can be divided exactly by 3.

the divisibility of (n-4) is the same with (n-4+3)=(n-1)

so, (n-1),(n),(n+1) are three consecutive integers

作者: XIAOHANMEIME 时间: 2006-8-9 18:27

懂了，原来是拆分：n (n+1) (n-4)= n (n+1) (n-1-3)= n (n+1) (n-1)-3 n (n+1)

都能被3整除

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