First Supplement to Law of Quadratic Reciprocity/Examples/19

Examples of First Supplement to Law of Quadratic Reciprocity

$-1$ is a quadratic non-residue of $19$.

Proof

We have that:

$19 = 4 \times 5 - 1$

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

The result follows from the First Supplement to Law of Quadratic Reciprocity.

$\blacksquare$

Sources

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