Consecutive Pairs of Quadratic Residues

Theorem

A particular theorem is missing. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by adding the theorem. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{TheoremWanted}} from the code.

Proof

This theorem requires a proof. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{ProofWanted}} from the code. If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.

Examples

Consecutive Pairs of Quadratic Residues of $3$

There are no modulo $3$.

This is consistent with the number of such being $\floor {\dfrac 3 4}$.

Consecutive Pairs of Quadratic Residues of $5$

There is $1$ modulo $5$.

This is consistent with the number of such being $\floor {\dfrac 5 4}$.

Consecutive Pairs of Quadratic Residues of $7$

There is $1$ modulo $7$.

This is consistent with the number of such being $\floor {\dfrac 7 4}$.

Consecutive Pairs of Quadratic Residues of $11$

There are $2$ modulo $11$.

This is consistent with the number of such being $\floor {\dfrac {11} 4}$.

Consecutive Pairs of Quadratic Residues of $17$

There are $4$ modulo $17$.

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

Consecutive Pairs of Quadratic Residues of $29$

There are $7$ modulo $29$.

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

Consecutive Pairs of Quadratic Residues of $61$

There are $15$ modulo $61$.

This is consistent with the number of such being $\floor {\dfrac {61} 4}$.