# Number theory - quadratic residues

1. Mar 17, 2012

### yeland404

1. The problem statement, all variables and given/known data

find all incongruent solutions of each quadratic congruence below.
X^2$\equiv$23 mod 77
2. Relevant equations
X^2$\equiv$11 mod 39

3. 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?

2. Mar 18, 2012