Show $c=rp^a$ is a quadratic residue modulo odd prime power $p^n$

Question

We are given:

1. odd prime $p$
2. $c=rp^a$, where $\gcd(r,p)=1 $ and $1< a<n$
3. Algorithm $A$ that solves $x^2 \equiv c'\bmod p^n$ for all $c'\in \mathbb Z_p$

Now, we wish to find the solutions for $x^2\equiv c\bmod p^n$.
Moreover, we want to find the exact number of solutions.

I didn't managed to reach a good solution. Any thoughts?