What are the remainders of a perfect square when divided by $5$ ?

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Solution

When perfect squares $9, 16, 25, 36, 49, 64$ are divided by $5$ the remainders are $4, 1, 0, 1, 4, 4$ respectively.
Therefore the remainders of a perfect square when divided by $5$ are $0, 1$ and $4$ .

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