Timeline for Does $\det\left[\left(\frac{i^2-\frac{p-1}2!\,j}p\right)\right]_{1\le i,j\le(p-1)/2}$ vanish for every prime $p\equiv3\pmod 4$?
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 8, 2018 at 8:59 | comment | added | Fedor Petrov | The second matrix is simply antisymmetric of odd order, but the first is not even if we permute the rows and columns (there are not enough many zero entries) | |
| Jun 8, 2018 at 4:58 | comment | added | Zhi-Wei Sun | By (1.16) of my paper arxiv.org/abs/1308.2900, for any prime $p\equiv 3\pmod 4$ we have $\det[(\frac{i^2-j^2}p)]_{1\le i,j\le(p-1)/2}=0$. | |
| Jun 8, 2018 at 4:57 | comment | added | Zhi-Wei Sun | @Amdeberhan Have you really proved the equivalence? | |
| Jun 8, 2018 at 4:35 | history | answered | T. Amdeberhan | CC BY-SA 4.0 |