被2或者3整除的一个题目

carbonzju · 发表于 2011-3-29 00:41:43

求解个题目，最好是简单做法哈，复杂的表要啦。[attachimg]85785[/attachimg]

sdcar2010 · 发表于 2011-3-29 06:25:13

No matter if it is a white cat or a black cat; as long as it can catch mice, it is a good cat.

1) n is odd. Let n = 3 and 11. Insufficient.
2) n is not 3*a. Let n = 4 and 23. Insufficient.

When 1) and 2) combined:
If n is odd, then n-1 and n+1 are both even. In addition, one of n-1 and n+1 has a factor of 4. So (n-1)*(n+1) has a factor of 8.
If n is not 3*a, then one of n-1 and n+1 is 3*b, or (n-1)*(n+1) has a factor of 3.
Since (n+1)*(n+1) = 3*8*c, then r=0

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tintinc · 发表于 2011-3-29 06:37:27

Good explanation!

被2或者3整除的一个题目

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