Timeline for Find all solution $a,b,c$ with $(1-a^2)(1-b^2)(1-c^2)=8abc$
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| Apr 13, 2017 at 12:19 | history | edited | CommunityBot |
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| Dec 7, 2015 at 13:56 | answer | added | Tito Piezas III | timeline score: 3 | |
| Jun 11, 2015 at 10:00 | answer | added | math110 | timeline score: 7 | |
| Jun 11, 2015 at 9:28 | history | edited | James Cranch | CC BY-SA 3.0 |
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| Jun 11, 2015 at 6:58 | answer | added | Allan MacLeod | timeline score: 11 | |
| Jun 7, 2015 at 3:09 | vote | accept | math110 | ||
| Jun 6, 2015 at 1:30 | history | edited | math110 | CC BY-SA 3.0 |
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| Jun 5, 2015 at 17:25 | answer | added | Joe Silverman | timeline score: 18 | |
| Jun 5, 2015 at 17:10 | comment | added | Joe Silverman | @AlexDegtyarev Noam's comment didn't answer the question of how to find/describe all rational solutions, although it could have been given as an answer (rather than a comment) for how to find infinitely many, and possibly how to find a Zariski dense set of solutions. But in any case, characterizing rational points on K3 surfaces certainly qualifies as a research-level problem, and this seems like a nice example due to the symmetry. | |
| Jun 5, 2015 at 17:08 | history | reopened |
Stefan Kohl♦ Joseph O'Rourke Derek Holt Ricardo Andrade Joe Silverman |
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| Jun 5, 2015 at 16:09 | history | edited | math110 | CC BY-SA 3.0 |
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| Jun 5, 2015 at 15:40 | review | Reopen votes | |||
| Jun 5, 2015 at 17:10 | |||||
| Jun 5, 2015 at 15:21 | history | edited | math110 | CC BY-SA 3.0 |
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| Jun 5, 2015 at 15:21 | comment | added | math110 | why closed it this question? | |
| Jun 5, 2015 at 15:01 | comment | added | math110 | But you papers,But I can't understand why can solve my problem,can you explain? | |
| Jun 5, 2015 at 10:14 | history | closed |
Will Jagy Alex Degtyarev Daniel Loughran Stefan Kohl♦ Carlo Beenakker |
Not suitable for this site | |
| Jun 5, 2015 at 10:10 | comment | added | Alex Degtyarev | @GerryMyerson: Just the opposite for me :) A citation from one of my papers: "Thanks to the global Torelli theorem, any reasonable geometric question about $K3$-surfaces can eventually be answered, given time" :) But this one is even easier: $K3$ is not rational! | |
| Jun 5, 2015 at 10:06 | comment | added | Gerry Myerson | @Alex, any answer that starts with "It's a K3 surface" is research level (and not at all obvious) to me. | |
| Jun 5, 2015 at 10:04 | comment | added | Alex Degtyarev | @GerryMyerson (a) this seems to be the tradition, (b) an answer fitting to a comment is likely to indicate that the question is not research level in the first place, (c) the particular answer given is, indeed, almost obvious. | |
| Jun 5, 2015 at 9:52 | comment | added | Gerry Myerson | @Alex, I don't understand. Why is an answer in a comment a reason for closure as off-topic? | |
| Jun 5, 2015 at 7:33 | comment | added | Alex Degtyarev | I'm voting to close this question as off-topic because it has been answered in a comment. | |
| Jun 5, 2015 at 1:49 | review | Close votes | |||
| Jun 5, 2015 at 10:16 | |||||
| Jun 5, 2015 at 1:25 | comment | added | Noam D. Elkies | It's a K3 surface, so you cannot give a complete rational parametrization; but there are enough elliptic fibrations that once you've found a few solutions you can probably bounce them around to get infinitely many others (e.g. from a typical solution you get three others by fixing two of the variables and finding the other solution for the third; now choose another variable and repeat). | |
| Jun 5, 2015 at 1:17 | history | asked | math110 | CC BY-SA 3.0 |