证明:若n为整数,则(2n+1)²-(2n-1)²一定能被8整除.

问题描述:

证明:若n为整数,则(2n+1)²-(2n-1)²一定能被8整除.

(2n+1)^2-(2n-1)^2
=[(2n+1)+(2n-1)][(2n+1)- (2n-1)]]
=(4n)×2
=8n
因为n不为0,所以8n一定是8的倍数,即8n能被8整除 .