Consecutive Pairs of Quadratic Residues/Examples/11
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Examples of Consecutive Pairs of Quadratic Residues
There are $2$ consecutive pairs of quadratic residues modulo $11$.
This is consistent with the number of such consecutive pairs being $\floor {\dfrac {11} 4}$.
Proof
From Quadratic Residues modulo $11$:
- $\set {1, 3, 4, 5, 9}$ are the quadratic residues modulo $11$
The set of pairs of consecutive quadratic residues modulo $11$ is therefore:
- $\set {\set {3, 4}, \set {4, 5} }$
The result follows.
$\blacksquare$
Sources
- 1971: George E. Andrews: Number Theory ... (previous) ... (next): $\text {3-5}$ The Use of Computers in Number Theory: Exercise $7$