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
From Quadratic Residues modulo $3$:


 * $1$ 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.