Consecutive Pairs of Quadratic Residues/Examples/17

Examples of Consecutive Pairs of Quadratic Residues

There are $4$ consecutive pairs of quadratic residues modulo $17$.

This is consistent with the number of such consecutive pairs being $\floor {\dfrac {17} 4}$.

Proof

From Quadratic Residues modulo $17$:

$\set {1, 2, 4, 8, 9, 13, 15, 16}$ are the quadratic residues modulo $17$

The set of pairs of consecutive quadratic residues modulo $17$ is therefore:

$\set {\set {1, 2}, \set {8, 9}, \set {15, 16}, \set {16, 1} }$

The result follows.

$\blacksquare$

Sources

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