Timeline for How can I solve a cubic equation in a finite field with characteristic 2?
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
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| S May 16, 2014 at 19:25 | history | suggested | Jyrki Lahtonen | CC BY-SA 3.0 |
TeX bug - sorry about not catching it right away.
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| May 16, 2014 at 19:23 | review | Suggested edits | |||
| S May 16, 2014 at 19:25 | |||||
| S May 16, 2014 at 19:19 | history | suggested | Jyrki Lahtonen | CC BY-SA 3.0 |
Some TeXifying
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| May 16, 2014 at 19:17 | review | Suggested edits | |||
| S May 16, 2014 at 19:19 | |||||
| Apr 13, 2014 at 1:39 | comment | added | Gerry Myerson | In the comment about 08, are you using the symbol $a$ to mean two different things, a "prime element" and the coefficient of $x^2$? | |
| Apr 12, 2014 at 4:56 | comment | added | user13113 | IIRC, you can repeat the derivation of the cubic formula. | |
| Apr 12, 2014 at 0:20 | answer | added | Noam D. Elkies | timeline score: 28 | |
| Apr 11, 2014 at 23:19 | comment | added | Dimitri | @Felipe: You are right, that was my mistake. This answers my question. Thank you very much. | |
| Apr 11, 2014 at 23:19 | review | Close votes | |||
| Apr 12, 2014 at 10:32 | |||||
| Apr 11, 2014 at 23:04 | review | First posts | |||
| Apr 11, 2014 at 23:15 | |||||
| Apr 11, 2014 at 23:03 | comment | added | Dimitri | Yes certainly it is possible. The point of the example was to demonstrate that there are cubic equations that have solutions for which (a^2 + b) does not have a sq root. The 08 is the hex representation of a GF(2^5) element - in binary form it would be '01000', equal to a^3, a being the prime element. This equation does have (at least) one root: For x=10 ('1000' = a^4) it becomes zero, yet (a^2+b) which is equal to b (=08=a^3) in this case does not have a square root because it equals an odd power of a. | |
| Apr 11, 2014 at 23:01 | comment | added | Felipe Voloch | Every element has a square root in a finite field of even order. | |
| Apr 11, 2014 at 22:56 | comment | added | Gerry Myerson | I don't know what 08 is (a coefficient in your example cubic). But it's possible that a cubic has no solution in a given finite field, right? Anyway, MO is for math research --- I don't see where there's a research angle to your question. | |
| Apr 11, 2014 at 22:45 | history | asked | Dimitri | CC BY-SA 3.0 |