For which positive integers $n$ is it true that
$$1^2 + 2^2 + \cdots + (n − 1)^2 \equiv 0 \,(\text{mod } n)$$
I have no idea where to start. I'm just looking for a nudge in the right direction. Any idea how to go about solving? Thanks for any help.
For which positive integers $n$ is it true that
$$1^2 + 2^2 + \cdots + (n − 1)^2 \equiv 0 \,(\text{mod } n)$$
I have no idea where to start. I'm just looking for a nudge in the right direction. Any idea how to go about solving? Thanks for any help.
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