Timeline for Construction of an irreducible polynomial on $\mathbb{Z}[x]$
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 4 at 2:46 | vote | accept | jack | ||
| Sep 1 at 8:20 | answer | added | Aleksei Kulikov | timeline score: 8 | |
| Aug 31 at 19:08 | comment | added | jack | @AlekseiKulikov Could you please give some more details? How do you make the sum of $n$'th powers divisible by $m$? If all conjugates are positive how is it possible to ensure that $P(x)$ has only integer coefficients? | |
| Aug 31 at 13:59 | comment | added | Aleksei Kulikov | It's likely an exercise on the standard trick of an algebraic number, all of whose conjugates have absolute value less than one (Pisot–Vijayaraghavan number), if in addition all the conjugates are positive, then the floor of $1+r^n$ is equal to the sum of $n$'th powers, which can also be made divisible by $m$. Not sure if this is appropriate for MO, the trick is standard but there is a lot of details to fill in. | |
| Aug 31 at 13:41 | history | asked | jack | CC BY-SA 4.0 |