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

Lola Thompson^{[1]}

- [1] Department of Mathematics Oberlin College Oberlin, OH 44074 USA

Journal de Théorie des Nombres de Bordeaux (2014)

- Volume: 26, Issue: 1, page 253-267
- ISSN: 1246-7405

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topThompson, 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 -

## References

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