Timeline for Are there integer solutions of $m^4+m^2n^2+n^4=k^2$?
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 21 at 13:16 | answer | added | Peter Mueller | timeline score: 11 | |
| Nov 21 at 10:59 | vote | accept | Wolfgang | ||
| Nov 21 at 10:40 | answer | added | François Brunault | timeline score: 10 | |
| Nov 21 at 10:16 | comment | added | François Brunault | This reduces to the quartic curve $y^2 = x^4+x^2+1$ which has the (non-singular) rational point $(0,1)$, so is birational to an elliptic curve $E$. One finds $E=48a1$, whose Mordell-Weil group is $\mathbf{Z}/2\mathbf{Z} \times \mathbf{Z}/2\mathbf{Z}$ so I guess there is no non-trivial solution. | |
| Nov 21 at 8:46 | history | asked | Wolfgang | CC BY-SA 4.0 |