Timeline for Pythagorean triples related to non-isometric equidistant plane quadruples
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 1, 2013 at 3:23 | comment | added | Noam D. Elkies | Wlodzimierz Holsztynski: You're welcome! As it happens this was the second time this week that I was asked about a Diophantine equation that turned out to reduce to this Fermat curve... @Barry Cipra: you're right, and Fermat already did it! He proved that neither $x^4+y^4=z^2$ nor $x^4+y^2=z^4$ has nontrivial rational solutions. The former curve is isomorphic with $y^2=x^3-4x$ and isogenous with $y^2=x^3+x$; the latter, isomorphic with $y^2=x^3+4x$ and isogenous with $y^2=x^3-x$. | |
| Jun 27, 2013 at 21:48 | comment | added | Barry Cipra | If I'm correct, Fermat's proof by descent that $x^4+y^4=z^2$ has no solutions can be adapted to the equation $4x^4+u^4=y^2$. It's just a matter of paying careful attention to the 2's. | |
| Jun 27, 2013 at 21:41 | comment | added | Włodzimierz Holsztyński | Noam, that was fast (8 minutes according to the official OM time) and sharp. Thank you. | |
| Jun 27, 2013 at 21:37 | vote | accept | Włodzimierz Holsztyński | ||
| Jun 27, 2013 at 21:23 | history | answered | Noam D. Elkies | CC BY-SA 3.0 |