Timeline for find all of rational solutions of the quartic equation?
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 28, 2020 at 13:04 | comment | added | Luis Ferroni | Well I only guided you through a path that can be useful (at least to try to find other non-trivial solutions). It's up to you to fill the details and see if it works. | |
| Jan 28, 2020 at 11:27 | comment | added | user151553 | Thank you for the above comments. But I do not understsnd it completely..Does it yield a solution to the problem? | |
| Jan 27, 2020 at 15:12 | comment | added | GH from MO | SAGE tells that your second display defines an elliptic curve, which is isomorphic to the one defined by $y^2=x^3+8$. SAGE also tells that this elliptic curve has infinitely many rational points. Relevant SAGE commands: "a, b = polygen(QQ, 'a, b')", "E = Jacobian(b^2-2*a^4-2*a)", "print E", "print E.mwrank()". | |
| Jan 27, 2020 at 14:48 | history | answered | Luis Ferroni | CC BY-SA 4.0 |