P-adic integers and roots of unity

number-theory p-adic-number-theory

Hint: use Hensel's lemma. $\text{ }$

Added because you made an effort:

Second hint: what are the roots of $x^{p-1}-1$ in $\mathbf F_p$?

Third hint: for which $p$ does $x^2+1$ have a root in $\mathbf F_p$?

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