$p$ is a prime number.
How to tell if a system of congruences:
\begin{align} x &\equiv a_1 \pmod{p^{i_1}} \\ x&\equiv a_2 \pmod{p^{i_2}} \\ &\dots\\ x &\equiv a_n \pmod{p^{i_n}} \end{align}
Has a solution.
How would you find the solution?
I feel like it has something to do with the chinese remainder theorem but the mod bases are definitely not pairwise relatively prime