First Supplement to Law of Quadratic Reciprocity/Examples/19
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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 $6$