First Supplement to Law of Quadratic Reciprocity/Examples/7

Examples of First Supplement to Law of Quadratic Reciprocity

 * $-1$ is a quadratic non-residue of $7$.

Proof
From Quadratic Residues of 7:


 * the set of quadratic residues modulo $7$ is:
 * $\set {1, 2, 4}$
 * but not $6 \equiv -1 \pmod 7$.

We also have that:
 * $7 = 4 \times 2 - 1$

and so is not of the form $4 n + 1$.