First Supplement to Law of Quadratic Reciprocity/Examples/3

Examples of First Supplement to Law of Quadratic Reciprocity

 * $-1$ is a quadratic non-residue of $3$.

Proof
From Quadratic Residues of 3:


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

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

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