need help on quadratic reciprocity
Prove that the quadratic residues of 11 are 1,3,4,5,9, and list all solutions of each of the ten congruences
and where a=1,3,4,5,9.
i used Legendre to show (1/11)=1,...,(9/11)=1, for i used legendre again to show a=1,3,4,5,9 are quadratic residues of .
My problem is with the second part have no idea how to even begin.
Quadratic residues form a repeating pattern
, , , , , , , , , ,
So the solutions for the first part are:
x=1+11k or x=10+11k
x=5+11k or x=6+11k
x=2+11k or x=9+11k
x=4+11k or x=7+11k
x=3+11k or x=8+11k