# Prove: if $n$ is a positive integer, then $n^2$ is divisible by 3 with remainder either $0$ or $1$ [duplicate]

Possible Duplicate:
Would like a proofreading of my proof

Prove that if $n$ is positive integer, then $n^2$ is divisible by $3$ with remainder either $0$ or $1$.

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## marked as duplicate by Jyrki Lahtonen♦, Srivatsan, Quixotic, Rasmus, mixedmath♦Oct 23 '11 at 16:33

If this is homework, please use the [homework] tag. –  Srivatsan Oct 23 '11 at 14:36
a duplicate –  Jyrki Lahtonen Oct 23 '11 at 14:53
@evodevo: Don't take it personally that this is being closed. A house rule. I'm sure you will learn enough by studying the answers of the duplicate question. –  Jyrki Lahtonen Oct 23 '11 at 18:02

Hint: $$0^2=0\mod 3,$$
$$1^2=1\mod 3,$$
$$2^2=4=1\mod 3.$$