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How can I prove that square of every integer is of the form either $3k+1$ or $3k$, but not $3k+2$?

My approach

I considered first, the integer $n$ to be even and then $n= 2m$; and if $n$ is odd then $n=2m+1$ but this step takes me to nowhere. I get usually stuck in these kind of questions. and this time I seriously need help . So, please post answer in detail and also mention how and why you arrived at that particular step. Thanks in advance.

  • 0
    I did not see you take the square of the integers you made.2012-07-24
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    Take $n=3k$ or $n=3k\pm 1$2012-07-24
  • 0
    Nearly the same: http://math.stackexchange.com/questions/172535/use-the-division-algorithm-to-show-the-square-of-any-integer-is-in-the-form-3k2012-07-24

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