Consecutive Pairs of Quadratic Residues/Examples/5

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Examples of Consecutive Pairs of Quadratic Residues

There is $1$ consecutive pair of quadratic residues modulo $5$.

This is consistent with the number of such consecutive pairs being $\floor {\dfrac 5 4}$.


Proof

From Quadratic Residues modulo $5$:

$4$ and $1$ are quadratic residue
$2$ and $3$ are not quadratic residues.

In this context $4$ and $1$ are considered a pair of consecutive quadratic residues.

The result follows.

$\blacksquare$


Sources