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 $4 n + 1$.

$\blacksquare$

Sources

• 1971: George E. Andrews: Number Theory ... (previous) ... (next): $\text {4-1}$ Basic Properties of Congruences: Exercise $6$