Consecutive Pairs of Quadratic Residues/Examples/7
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Examples of Consecutive Pairs of Quadratic Residues
There is $1$ consecutive pair of quadratic residues modulo $7$.
This is consistent with the number of such consecutive pairs being $\floor {\dfrac 7 4}$.
Proof
From Quadratic Residues modulo $7$:
- $\set {1, 2, 4}$ are the quadratic residues modulo $7$
The only pair of consecutive quadratic residues is therefore $\set {1, 2}$.
The result follows.
$\blacksquare$
Sources
- 1971: George E. Andrews: Number Theory ... (previous) ... (next): $\text {3-5}$ The Use of Computers in Number Theory: Exercise $7$