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
- 1971: George E. Andrews: Number Theory ... (previous) ... (next): $\text {3-5}$ The Use of Computers in Number Theory: Exercise $7$