Quadratic Residue/Examples/17

Example of Quadratic Residues
The set of quadratic residues modulo $17$ is:
 * $\set {1, 2, 4, 8, 9, 13, 15, 16}$

Proof
To list the quadratic residues of $17$ it is enough to work out the squares $1^2, 2^2, \dotsc, 16^2$ modulo $17$.

So the set of quadratic residues modulo $17$ is:
 * $\set {1, 2, 4, 8, 9, 13, 15, 16}$

The set of quadratic non-residues of $17$ therefore consists of all the other non-zero least positive residues:
 * $\set {3, 5, 6, 7, 10, 11, 12, 14}$