Timeline for Primitive integral solutions to $x^2+y^3=z^2$
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 17, 2020 at 21:38 | history | edited | YCor | CC BY-SA 4.0 |
removed capitals from title (the question was bumped anyway)
|
| Oct 17, 2020 at 17:30 | history | edited | Pietro Paparella | CC BY-SA 4.0 |
Improved exposition
|
| Feb 9, 2018 at 4:03 | vote | accept | Pietro Paparella | ||
| Mar 15, 2017 at 7:47 | answer | added | Włodzimierz Holsztyński | timeline score: 4 | |
| Mar 15, 2017 at 5:13 | answer | added | Zurab Silagadze | timeline score: 11 | |
| Mar 15, 2017 at 4:44 | comment | added | individ | The parameterization equation $x^2+y^3=z^2$ can record such. artofproblemsolving.com/community/c3046h1217955_the_cube_view For $x^2+y^3=z^4$ artofproblemsolving.com/community/… As already said - it is better for each individual degree to solve directly the equation. | |
| Mar 15, 2017 at 3:57 | comment | added | Pietro Paparella | @NoamD.Elkies: there are references but they concern the cases when $3 \leq n \leq 5$. | |
| Mar 15, 2017 at 3:21 | comment | added | Noam D. Elkies | The last, and by far the hardest, case is $n=5$, which is solved in: J. Edwards: A Complete Solution to $X^2 + Y^3 + Z^5 = 0$, Journal f. d. reine und angew. Math. (Crelle's Journal) 571 (2004), 213-236. (Change $(X,Y,Z)$ to $(x,y,-z)$ for your form of the equation.) That paper should also give references for $n<5$. | |
| Mar 15, 2017 at 2:54 | history | edited | Pietro Paparella | CC BY-SA 3.0 |
Reference added
|
| Mar 15, 2017 at 2:39 | history | edited | Pietro Paparella | CC BY-SA 3.0 |
edited body
|
| Mar 15, 2017 at 2:33 | comment | added | Gerhard Paseman | You can treat this as a special case of factoring, e.g. $Y=(z+x)(z-x)$, where you can have one of the factors (say $z-x$) be $y$ to a power. If you want everything integral, make sure the factors have the same parity. Gerhard "Difference Of Squares Is Easy" Paseman, 2017.03.14. | |
| Mar 15, 2017 at 2:21 | history | edited | Pietro Paparella | CC BY-SA 3.0 |
title edited
|
| Mar 15, 2017 at 2:16 | history | asked | Pietro Paparella | CC BY-SA 3.0 |