First Supplement to Law of Quadratic Reciprocity/Examples/7
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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 $6$