Consecutive Pairs of Quadratic Residues/Examples/29

Examples of Consecutive Pairs of Quadratic Residues
There are $7$ consecutive pairs of quadratic residues modulo $29$.

This is consistent with the number of such consecutive pairs being $\floor {\dfrac {29} 4}$.

Proof
From Quadratic Residues modulo $29$:


 * $\set {1, 4, 5, 6, 7, 9, 13, 16, 20, 22, 23, 24, 25, 28}$ are the quadratic residues modulo $29$

The set of pairs of consecutive quadratic residues modulo $29$ is therefore:
 * $\set {\set {4, 5}, \set {5, 6}, \set {6, 7}, \set {22, 23}, \set {23, 24}, \set {24, 25}, \set {28, 1} }$

The result follows.