First Supplement to Law of Quadratic Reciprocity/Examples/11

Examples of First Supplement to Law of Quadratic Reciprocity

 * $-1$ is a quadratic non-residue of $11$.

Proof
From Quadratic Residues of 11:


 * the set of quadratic residues modulo $11$ is:
 * $\set {1, 3, 4, 5, 9}$
 * but not $10 \equiv -1 \pmod {11}$.

We also have that:
 * $11 = 4 \times 3 - 1$

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