If n is an odd positive integer, what is the remainder when(n2-1 )is divided by 8?

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问题 If n is an odd positive integer, what is the remainder when(n²-1 )is divided by 8?

选项 A、l
B、0
C、5
D、4
E、6

答案B

解析如果用代入法来做最简单。比如随便选择一个奇数3，9-1=8，因此除以8余数为0。如果按照原理来做，则是n²-1=(n-1)(n+1)，由于n是奇数，所以n-1和n+1是两个连续的正偶数，两个连续的正偶数的乘积必然是8的倍数，所以除以8余数为0。选择B。

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If n is an odd positive integer, what is the remainder when(n2-1 )is divided by 8?

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