# If $p \equiv 1 \pmod 4$ where $p$ is an odd prime, then $x^2 \equiv -1 \pmod {p^k}$ where $k$ is any integer has $2$ solutions. [closed]

How can I prove that the equation $$x^2 \equiv -1 \pmod {p^k}$$, where $$p$$ is an odd prime and $$p \equiv 1 \pmod 4$$ and $$k$$ is any integer, has exactly two solutions?

Thank you!

## closed as off-topic by Carl Mummert, YiFan, John Omielan, Leucippus, CesareoMar 2 at 0:51

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