If a is an odd number,then there must exist an integer such that a²-1=()求数学答案A.3n,B.5n,C.8n ,D.16n选择

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If a is an odd number,then there must exist an integer such that a²-1=()求数学答案A.3n,B.5n,C.8n ,D.16n选择
If a is an odd number,then there must exist an integer such that a²-1=()求数学答案
A.3n,B.5n,C.8n ,D.16n
选择

If a is an odd number,then there must exist an integer such that a²-1=()求数学答案A.3n,B.5n,C.8n ,D.16n选择
a²-1=4n,因为 a²-1=(a-1)(a+1),条件给出a是奇数,所以a-1和a+1均为偶数,即 a²-1为4的倍数.又因为(a+1)-(a-1)=2,所以(a+1)/2-(a-1)/2=1,所以(a+1)/2与(a-1)/2为两个相邻的整数,其奇偶性相反,所以[(a+1)/2]×[(a-1)/2]为2的倍数,不是4的倍数.
即﹙ a²-1﹚/4为2的倍数且不为4的倍数,即a²-1为8的倍数不为16的倍数.所以选C.

其实既然是选择题,那最简单的方法就是随便找几个奇数算一下,总是符合规律的就是正确的了

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