Quadratic Residue/Examples/7

Example of Quadratic Residues
The set of quadratic residues modulo $7$ is:
 * $\set {1, 2, 4}$

Proof
To list the quadratic residues of $7$ it is enough to work out the squares $1^2, 2^2, \dotsc, 6^2$ modulo $7$.

So the set of quadratic residues modulo $7$ is:
 * $\set {1, 2, 4}$

The set of quadratic non-residues of $7$ therefore consists of all the other non-zero least positive residues:
 * $\set {3, 5, 6}$