Consecutive Pairs of Quadratic Residues/Examples/7

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 $7$