Timeline for Irreducible polynomial with roots mod p for all but finitely many p
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Aug 6, 2023 at 19:50 | comment | added | GH from MO | If you like my answer, please accept it officially (so that it turns green). Thanks in advance! | |
| Jul 27, 2023 at 12:36 | history | became hot network question | |||
| Jul 27, 2023 at 7:05 | comment | added | GH from MO | Please use a high-level tag like "nt.number-theory". I added this tag now. | |
| Jul 27, 2023 at 7:04 | history | edited | GH from MO |
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| Jul 27, 2023 at 6:59 | answer | added | GH from MO | timeline score: 13 | |
| Jul 27, 2023 at 5:31 | comment | added | Peter Mueller | Yes, as suggested by Fedor Petrov: Even the weaker Frobenius density theorem (see link.springer.com/article/10.1007/BF02839049 or isibang.ac.in/~sury/frobreso.pdf) shows that each element of the Galois group has a fixed point. Then by an easy theorem of Jordan, the Galois group is intransitive (or the polynomial is linear). Note that the orbits of the Galois group correspond to the irreducible factors of the polynomial. | |
| Jul 27, 2023 at 4:34 | comment | added | Fedor Petrov | Does not this follow from Chebotarev (or even earlier) density theorem? | |
| Jul 27, 2023 at 4:28 | history | asked | Joe Shipman | CC BY-SA 4.0 |