Quadratic Residue/Examples/11

Example of Quadratic Residues
The set of quadratic residues modulo $11$ is:
 * $\set {1, 3, 4, 5, 9}$

Proof
To list the quadratic residues of $11$ it is enough to work out the squares $1^2, 2^2, \ldots, 10^2$ modulo $11$.

So the set of quadratic residues modulo $11$ is:
 * $\set {1, 3, 4, 5, 9}$

The set of quadratic non-residues of $11$ therefore consists of all the other non-zero least positive residues:
 * $\set {2, 6, 7, 8, 10}$