Timeline for Solving equations in a subset of rational numbers
Current License: CC BY-SA 3.0
3 events
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| Nov 20, 2012 at 23:49 | comment | added | Xander Faber | The next thing I would do is to start exploring the geometry of these surfaces to get a better sense of what to expect. For example, is the projective closure smooth? A smooth hypersurface in $\mathbb{P}^3$ of degree at least 5 is of general type, so the Bombieri/Lang conjecture implies that all but finitely many of its rational points will lie on rational and elliptic curves on the surface. If that's the case, then finding the rational points is likely to be tricky. | |
| Nov 20, 2012 at 23:03 | comment | added | Max Alekseyev | Thanks! I've tried this approach but I also have no idea what to do with the resulting high-degree Diophantine equations. I would probably give up if I had just an equation like the one you derived. But I hope that the original formulation may provide additional insights into the structure of solutions and somehow simplify their search. | |
| Nov 20, 2012 at 19:49 | history | answered | Xander Faber | CC BY-SA 3.0 |