# Divide by $5$

If $n$ is a positive integer, then $n$ has $5$ possible remainders after division by five: $0, 1, 2, 3$ and $4$.

If $n$ is a positive integer, then $n^2$ is also a positive integer.

$n$ is a positive integer. What is the number of possible remainders of $n^2$ after division by five?

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