gwd-26-16

XIAOHANMEIME

 

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？       

XIAOHANMEIME

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

dbearwangs

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