Consecutive Pairs of Quadratic Residues
Theorem
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Proof
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Examples
Consecutive Pairs of Quadratic Residues of $3$
There are no Consecutive Pairs of Quadratic Residues modulo $3$.
This is consistent with the number of such consecutive pairs being $\floor {\dfrac 3 4}$.
Consecutive Pairs of Quadratic Residues of $5$
There is $1$ consecutive pair of quadratic residues modulo $5$.
This is consistent with the number of such consecutive pairs being $\floor {\dfrac 5 4}$.
Consecutive Pairs of Quadratic Residues of $7$
There is $1$ consecutive pair of quadratic residues modulo $7$.
This is consistent with the number of such consecutive pairs being $\floor {\dfrac 7 4}$.
Consecutive Pairs of Quadratic Residues of $11$
There are $2$ consecutive pairs of quadratic residues modulo $11$.
This is consistent with the number of such consecutive pairs being $\floor {\dfrac {11} 4}$.
Consecutive Pairs of Quadratic Residues of $17$
There are $4$ consecutive pairs of quadratic residues modulo $17$.
This is consistent with the number of such consecutive pairs being $\floor {\dfrac {17} 4}$.
Consecutive Pairs of Quadratic Residues of $29$
There are $7$ consecutive pairs of quadratic residues modulo $29$.
This is consistent with the number of such consecutive pairs being $\floor {\dfrac {29} 4}$.
Consecutive Pairs of Quadratic Residues of $61$
There are $15$ consecutive pairs of quadratic residues modulo $61$.
This is consistent with the number of such consecutive pairs being $\floor {\dfrac {61} 4}$.