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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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Hint: $$ 0^2=0\mod 3, $$

$$ 1^2=1\mod 3, $$

$$ 2^2=4=1\mod 3. $$

Rasmus
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