Quadratic Residue/Examples

Examples of Quadratic Residues

Quadratic Residues Modulo $3$

There exists exactly $1$ quadratic residue modulo $3$, and that is $1$.

Quadratic Residues Modulo $5$

The set of quadratic residues modulo $5$ is:

$\set {1, 4}$

Quadratic Residues Modulo $7$

The set of quadratic residues modulo $7$ is:

$\set {1, 2, 4}$

Quadratic Residues Modulo $11$

The set of quadratic residues modulo $11$ is:

$\set {1, 3, 4, 5, 9}$

Quadratic Residues Modulo $17$

The set of quadratic residues modulo $17$ is:

$\set {1, 2, 4, 8, 9, 13, 15, 16}$

Quadratic Residues Modulo $29$

The set of quadratic residues modulo $29$ is:

$\set {1, 4, 5, 6, 7, 9, 13, 16, 20, 22, 23, 24, 25, 28}$

Quadratic Residues Modulo $61$

The set of quadratic residues modulo $61$ is:

$\set {1, 3, 4, 5, 9, 12, 13, 14, 15, 16, 19, 20, 22, 25, 27, 34, 36, 39, 41, 42, 45, 46, 47, 48, 49, 53, 56, 57, 58, 60}$