Consecutive Pairs of Quadratic Residues/Examples/11

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 $7$