First Supplement to Law of Quadratic Reciprocity/Examples/17

Examples of First Supplement to Law of Quadratic Reciprocity

$-1$ is a quadratic residue of $17$.

Proof

From Quadratic Residues of 17:

the set of quadratic residues modulo $13$ is:

$\set {1, 2, 4, 8, 9, 13, 15, 16}$

and so $-1 \equiv 16 \pmod {17}$ is therefore a quadratic residue of $17$.

We also have that:

$17 = 4 \times 4 + 1$

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

$\blacksquare$

Sources

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