Timeline for The Diophantine equation $x^p - 4y^p = z^2$
Current License: CC BY-SA 3.0
15 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 20, 2014 at 9:10 | comment | added | Gerry Myerson | @Dietrich, there are more where those came from, I think eight examples with $x<1000$. | |
| Aug 20, 2014 at 8:45 | comment | added | Dietrich Burde | @GerryMyerson Your examples are also helpful here. | |
| Aug 20, 2014 at 4:07 | history | edited | Lucia |
Added top level tag
|
|
| Aug 20, 2014 at 3:56 | comment | added | Lucia | @FelipeVoloch: Good point! | |
| Aug 20, 2014 at 3:55 | comment | added | Felipe Voloch | @Lucia The finiteness of Darmon and Granville is for fixed $p$. ABC implies finiteness even if $p$ is allowed to vary. Of course, the results you cite in your answer settle the matter. | |
| Aug 20, 2014 at 3:48 | vote | accept | Yes | ||
| Aug 20, 2014 at 3:40 | answer | added | Lucia | timeline score: 9 | |
| Aug 20, 2014 at 3:34 | comment | added | Lucia | Well if there were infinitely many solutions, it would contradict a Theorem of Darmon and Granville! See math.mcgill.ca/darmon/pub/Articles/Research/12.Granville/… . | |
| Aug 20, 2014 at 3:14 | comment | added | Felipe Voloch | If there were infinitely many, it would contradict the abc conjecture. | |
| Aug 20, 2014 at 2:02 | comment | added | Gerry Myerson | Note that my earlier comment referred to an earlier version of the question. | |
| Aug 20, 2014 at 2:00 | history | edited | Yes | CC BY-SA 3.0 |
edited body
|
| Aug 20, 2014 at 2:00 | comment | added | Yes | Ah fantastic. Appreciated. Then I have to strengthen the lower bound. The first version of my question is for $p \geq 3,$ and that's why Gerry Myerson left the comment. | |
| Aug 20, 2014 at 1:59 | comment | added | Gerry Myerson | $78^3-4\times29^3=614^2$. $93^3-4\times53^3=457^2$. | |
| Aug 20, 2014 at 1:53 | review | First posts | |||
| Aug 20, 2014 at 2:44 | |||||
| Aug 20, 2014 at 1:51 | history | asked | Yes | CC BY-SA 3.0 |