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99999是不是三的倍数
更新时间： 2021-02-24 19:44:01  

1、99999是三的倍数。

2、解题方法：设这个数表示成x = 10^n * an + 10^(n-1) * a(n-1) + ...+ a1 (一共有n位)

那么只要证明x 与a1+a2+a3+...+an对于3同余即可

显然10^n * an - an = an * 99999.9999 能被3整除

所以10^n * an = an (mod 3)

同理 10^(n-1) * a(n-1) = a(n-1) (mod 3)

所以x = 10^n * an + 10^(n-1) * a(n-1) + ...+ a1 = an + a(n-1) + ...+ a1 (mod 3)

也就是x除以3的余数与x的各位数字和除以3的余数相同

所以如果各位数字和能被3整除,那么这个数就能被3整除。

关键词： 倍数

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