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.

Thanks in advance

  • $\begingroup$ You ask "is my solution correct?" but don't give your solution. $\endgroup$ – Lord Shark the Unknown Jun 22 '17 at 17:46
  • $\begingroup$ Sorry, you're right ! $\endgroup$ – pinkpanther5 Jun 22 '17 at 17:47
  • $\begingroup$ @LordSharktheUnknown:OK, in general, if I want to use the CRT on a quadratic residue , should I use $x$ or $x^2$? $\endgroup$ – pinkpanther5 Jun 22 '17 at 17:50
  • $\begingroup$ Let’s see your proposed solution to the problem, then one can attempt to judge its correctness. $\endgroup$ – Lubin Jun 22 '17 at 17:55
  • $\begingroup$ See here and here for some worked examples. $\endgroup$ – Bill Dubuque Jun 22 '17 at 20:12

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