Timeline for Roots of a polynomial in a finite field related to Fermat's Last Theorem
Current License: CC BY-SA 3.0
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10 events
| when toggle format | what | by | license | comment | |
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| Dec 8, 2014 at 10:29 | comment | added | Michael Stoll | You are welcome. -- I was suspecting that cube roots of unity might play a role (from the condition $l \equiv 1 \bmod 3$); looking at the first few cases confirmed that. | |
| Dec 8, 2014 at 2:30 | history | edited | TZE | CC BY-SA 3.0 |
simplified condition on P_l(x)
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| Dec 8, 2014 at 1:05 | comment | added | TZE | Wow! Thank you for the complete answer! Yes, I did. There were always at least two solutions excluding $0, 1.$ and they appeared in pairs $x, x^{-1}.$ Here is the Sage computation with the output: drive.google.com/file/d/0B_kUj8Mvy6_NUlNaLVg4VHJ0V1U/… | |
| Dec 8, 2014 at 0:26 | vote | accept | TZE | ||
| S Dec 7, 2014 at 17:02 | history | suggested | Michael Stoll |
Edited tags.
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| Dec 7, 2014 at 16:22 | review | Suggested edits | |||
| S Dec 7, 2014 at 17:02 | |||||
| Dec 7, 2014 at 11:28 | answer | added | Michael Stoll | timeline score: 20 | |
| Dec 7, 2014 at 10:02 | comment | added | Michael Stoll | Did you observe any patterns (e.g. regarding the number of roots or their location) in your computation? | |
| Dec 7, 2014 at 10:00 | comment | added | Michael Stoll | The condition on $P_l$ seems to be unnecessarily complicated. It is equivalent to $P_l$ not having any roots in ${\mathbb Z}/l{\mathbb Z}$ except possibly $0$ and/or $1$. | |
| Dec 7, 2014 at 6:34 | history | asked | TZE | CC BY-SA 3.0 |