Timeline for Sets of algebraic integers whose differences are units
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| S Jul 7 at 20:02 | vote | accept | Peter Kropholler | ||
| S Jul 7 at 20:02 | vote | accept | Peter Kropholler | ||
| S Jul 7 at 20:02 | |||||
| S Jul 4 at 6:54 | vote | accept | Peter Kropholler | ||
| S Jul 7 at 20:02 | |||||
| Jul 4 at 6:54 | vote | accept | Peter Kropholler | ||
| S Jul 4 at 6:54 | |||||
| Jun 29 at 3:34 | comment | added | Gerry Myerson | Nicholas Triantafillou, There are no exceptional units in number fields of degree prime to $3$ where $3$ splits completely, available at ngtriant.github.io/papers/no_exceptional_units_short_paper.pdf has an introduction which summarizes many results on exceptional units, with references. | |
| Jun 28 at 21:41 | answer | added | CHUAKS | timeline score: 5 | |
| Jun 27 at 15:25 | history | became hot network question | |||
| Jun 27 at 9:01 | comment | added | Chris Wuthrich | Look up exceptional sequences and exceptional units for this question in a fixed number field. | |
| Jun 27 at 8:26 | comment | added | Peter Taylor | @YCor, $x^2 + x - 1$ works up to $n=3$; $x^4 - x - 1$ works up to $n=5$; $x^6 - x^2 - 1$ works up to $n=7$. | |
| Jun 27 at 8:25 | answer | added | Henri Cohen | timeline score: 26 | |
| Jun 27 at 7:57 | comment | added | YCor | I imagine that for each $n$ there exists a unit $u$ such that $a_i=u^i$ works. But I could check it only for $n=3$ (e.g., $u$ root of $X^3-X+1$). | |
| Jun 27 at 7:40 | comment | added | YCor | @PeterTaylor $2$ is not a unit in the ring of algebraic integers. Units are algebraic numbers whose monic minimal polynomial is integral with $\pm 1$ constant coefficient. | |
| Jun 27 at 7:36 | comment | added | Peter Taylor | Isn't $0$ the only non-unit, so that any distinct integers work? | |
| Jun 27 at 7:31 | history | edited | YCor |
edited tags
|
|
| Jun 27 at 7:23 | history | asked | Peter Kropholler | CC BY-SA 4.0 |