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外语
If n is an odd positive integer, what is the remainder when(n2-1 )is divided by 8?
If n is an odd positive integer, what is the remainder when(n2-1 )is divided by 8?
admin
2021-10-21
27
问题
If n is an odd positive integer, what is the remainder when(n
2
-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n
2
-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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