First Supplement to Law of Quadratic Reciprocity/Examples/13

Examples of First Supplement to Law of Quadratic Reciprocity

 * $-1$ is a quadratic residue of $13$.

Proof
We have that:
 * $5^2 = 25 \equiv -1 \pmod 13$

and so $-1$ is therefore a quadratic residue of $13$.

We also have that:
 * $13 = 4 \times 3 + 1$

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