Quadratic Residue/Examples/29

Example of Quadratic Residues
The set of quadratic residues modulo $29$ is:
 * $\set {1, 4, 5, 6, 7, 9, 13, 16, 20, 22, 23, 24, 25, 28}$

Proof
From Square Modulo n Congruent to Square of Inverse Modulo n, to list the quadratic residues of $29$ it is sufficient to work out the squares $1^2, 2^2, \dotsc, \paren {\dfrac {28} 2}^2$ modulo $29$.

So:

So the set of quadratic residues modulo $29$ is:
 * $\set {1, 4, 5, 6, 7, 9, 13, 16, 20, 22, 23, 24, 25, 28}$

The set of quadratic non-residues of $29$ therefore consists of all the other non-zero least positive residues:
 * $\set {2, 3, 8, 10, 11, 12, 14, 15, 17, 18, 19, 21, 26, 27}$