How can I find (3) congruence equations to solve
$$x^2\equiv331\pmod{385}$$
using Legendre and Jacobi Symbols and use the Chinese Remainder Theorem to combine the solutions to those equations to produce the solutions to $x^2\equiv331\pmod{385}$
Solution
$$385=5\cdot7\cdot11$$
$$\begin{align} x^2&\equiv1\pmod5\\ x^2&\equiv2\pmod7\\ x^2&\equiv1\pmod{11}\\[10pt] x&\equiv\{1,4\}\pmod5\\ x&\equiv\{3,4\}\pmod7\\ x&\equiv\{1,10\}\pmod{11}\\ \end{align}$$
$$\begin{align} M1\implies&385/5=77\\ &77-1\pmod5=3\pmod5\\[5pt] M2\implies&385/7=55\\ &55-1\pmod7=6\pmod7\\[5pt] M2\implies&385/11=35\\ &35-1\pmod{11}=6\pmod{11}\\[5pt] \end{align}$$
$$a=1,4;\quad b=3,4;\quad c=1,10$$
$$\begin{align} x&\equiv a\cdot77\cdot3+b\cdot5\cdot6+c\cdot35\cdot6\\ &\equiv231a+330b+210c \end{align}$$
Therefore Congruence of 8 cases