Solution
= Solution
For $f(x)=x^2-n$, a root modulo the odd prime $p$ is nonzero because $p\nmid n$. Its derivative $2x$ is therefore nonzero modulo $p$. Part (i) gives exactly one lift of each root. A nonzero <quadratic residue> modulo an odd prime has two distinct roots, $x$ and $-x$; a nonresidue has none. Hence
$$
\boxed{\#\{x\pmod{p^l}:x^2\equiv n\}=1+\left(\frac np\right)\in\{0,2\}}.
$$