First Supplement to Law of Quadratic Reciprocity/Examples/5

Examples of First Supplement to Law of Quadratic Reciprocity

 * $-1$ is a quadratic residue of $5$.

Proof
From Quadratic Residues of 5:


 * the set of quadratic residues modulo $5$ is:
 * $\set {1, 4}$

We have that:
 * $4 \equiv -1 \pmod 5$

and so $-1$ is therefore a quadratic residue of $5$.

We also have that:
 * $5 = 4 \times 1 + 1$

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