Number theory - quadratic residues

[yeland404]

number theory -- quadratic residues

Homework Statement

find all incongruent solutions of each quadratic congruence below.
X^2$\equiv$23 mod 77

Homework Equations

X^2$\equiv$11 mod 39

The Attempt at a Solution

it is suffices to X^2$\equiv$23 mod 7, andX^2$\equiv$23 mod 11,
then how to do next?

 

[Karamata]

http://en.wikipedia.org/wiki/Chinese_remainder_theorem