# First Supplement to Law of Quadratic Reciprocity/Examples/3

Jump to navigation
Jump to search

## Examples of First Supplement to Law of Quadratic Reciprocity

- $-1$ is a quadratic non-residue of $3$.

## Proof

From Quadratic Residues of 3:

- there exists exactly $1$ quadratic residue modulo $3$, and that is $1$.

We also have that:

- $3 = 4 \times 1 - 1$

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 $6$