English

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

Number Theory 2012-06-21 v1

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 Z[x]. In this paper, we replace Z[x] with F_p[x], where p is an arbitrary-but-fixed prime. We also consider those n where this condition holds for all p.

Keywords

Cite

@article{arxiv.1206.4355,
  title  = {Variations on a question concerning the degrees of divisors of x^n-1},
  author = {Lola Thompson},
  journal= {arXiv preprint arXiv:1206.4355},
  year   = {2012}
}

Comments

Formerly part of arXiv:1111.5403