# Consecutive Pairs of Quadratic Residues/Examples/3

## Examples of Consecutive Pairs of Quadratic Residues

There are no Consecutive Pairs of Quadratic Residues modulo $3$.

This is consistent with the number of such consecutive pairs being $\floor {\dfrac 3 4}$.

## Proof

$1$ is a quadratic residue
$2$ is not a quadratic residue.

Hence neither is an element of a pair of consecutive quadratic residues.

The result follows.

$\blacksquare$