lean_workbook_plus_75702

Prove that $a$ is a quadratic residue $\bmod p^n$ if and only if the polynomial $x^2 - a \equiv 0 \bmod p^n$ has a solution. Also, prove that if $f(a) \equiv 0 \bmod p$ then a solution $\bmod p^2$ must reduce to a solution $\bmod p$.