Consecutive Pairs of Quadratic Residues

From ProofWiki
Jump to navigation Jump to search

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 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 $\floor {\dfrac {61} 4}$.

Retrieved from "https://proofwiki.org/w/index.php?title=Consecutive_Pairs_of_Quadratic_Residues&oldid=392371"