Variations on a question concerning the degrees of divisors of $x^n-1$

Thompson, Lola. "Variations on a question concerning the degrees of divisors of $x^n-1$." Journal de Théorie des Nombres de Bordeaux 26.1 (2014): 253-267. <http://eudml.org/doc/275785>.

@article{Thompson2014,
abstract = {In this paper, we examine a natural question concerning the divisors of the polynomial $x^n-1$: “How often does $x^n-1$ have a divisor of every degree between $1$ and $n$?” In a previous paper, we considered the situation when $x^n-1$ is factored in $\mathbb\{Z\}[x]$. In this paper, we replace $\mathbb\{Z\}[x]$ with $\{\mathbb\{F\}\}_p[x]$, where $p$ is an arbitrary-but-fixed prime. We also consider those $n$ where this condition holds for all $p$.},
affiliation = {Department of Mathematics Oberlin College Oberlin, OH 44074 USA},
author = {Thompson, Lola},
journal = {Journal de Théorie des Nombres de Bordeaux},
language = {eng},
month = {4},
number = {1},
pages = {253-267},
publisher = {Société Arithmétique de Bordeaux},
title = {Variations on a question concerning the degrees of divisors of $x^n-1$},
url = {http://eudml.org/doc/275785},
volume = {26},
year = {2014},
}

TY - JOUR
AU - Thompson, Lola
TI - Variations on a question concerning the degrees of divisors of $x^n-1$
JO - Journal de Théorie des Nombres de Bordeaux
DA - 2014/4//
PB - Société Arithmétique de Bordeaux
VL - 26
IS - 1
SP - 253
EP - 267
AB - In this paper, we examine a natural question concerning the divisors of the polynomial $x^n-1$: “How often does $x^n-1$ have a divisor of every degree between $1$ and $n$?” In a previous paper, we considered the situation when $x^n-1$ is factored in $\mathbb{Z}[x]$. In this paper, we replace $\mathbb{Z}[x]$ with ${\mathbb{F}}_p[x]$, where $p$ is an arbitrary-but-fixed prime. We also consider those $n$ where this condition holds for all $p$.
LA - eng
UR - http://eudml.org/doc/275785
ER -