First Supplement to Law of Quadratic Reciprocity/Examples/17

Examples of First Supplement to Law of Quadratic Reciprocity

 * $-1$ is a quadratic residue of $17$.

Proof
From Quadratic Residues of 17:


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

and so $-1 \equiv 16 \pmod {17}$ is therefore a quadratic residue of $17$.

We also have that:
 * $17 = 4 \times 4 + 1$

and so is of the form $4 n + 1$.