Timeline for Can the difference of two distinct Fibonacci numbers be a square infinitely often?
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Jan 5, 2013 at 1:24 | comment | added | David E Speyer | A finite union of genus zero curves (plus finitely many counterexamples), due to Siegel's theorem. I think that what joro was saying above was that there are no rational curves on this surface, but I may have misunderstood him. | |
| Jan 4, 2013 at 23:21 | comment | added | Joe Silverman | AFAIK, there are no proven major results on integer points on affine pieces of K3 surfaces. However, Vojta's conjecture predicts that the set of such points lies on a finite union of curves. So assuming Vojta's conjecture, one might be able to make further progress. | |
| Jan 6, 2012 at 13:22 | comment | added | joro | The package "desing" de-singularized the surface. If I have done it right I see no curves on it (and the remaining solutions must be quite large). | |
| Jan 6, 2012 at 13:13 | history | edited | David E Speyer | CC BY-SA 3.0 |
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| Jan 6, 2012 at 10:34 | comment | added | joro | Thank you. Is it possible $x^2-x y-y^2 = -1$ to be a typo?. I get $x^2-x y-y^2 = +1$ | |
| Jan 5, 2012 at 16:15 | history | answered | David E Speyer | CC BY-SA 3.0 |