# Quadratic residue with CRT ?

I'm given $$x^2\equiv a \pmod q$$ where $q=p_1\cdot p_2\cdot p_3$

I've rewrite it in a system of three and used the CRT on it and got a solution, but in the system I used $x$ instead of $x^2$.

Should have I done it with $x^2$ ? Because my solution doesn't work for the origin equation.

• @LordSharktheUnknown:OK, in general, if I want to use the CRT on a quadratic residue , should I use $x$ or $x^2$? – pinkpanther5 Jun 22 '17 at 17:50