On the order of the polynomial $x^p-x-a$

Xiwang Cao

Paper 2010/034

On the order of the polynomial $x^p-x-a$

Xiwang Cao

Abstract

In this note, we prove that the order of $x^p-x-1\in \F_p[x]$ is $\frac{p^p-1}{p-1}$, where $p$ is a prime and $\mathbb{F}_p$ is the finite field of size $p$. As a consequence, it is shown that $x^p-x-a\in \mathbb{F}_p[x]$ is primitive if and only if $a$ is a primitive element in $\mathbb{F}_p$.

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Published elsewhere. Unknown where it was published
Contact author(s): xwcao @ nuaa edu cn
History: 2010-01-22: received
Short URL: https://ia.cr/2010/034
License: CC BY

BibTeX

@misc{cryptoeprint:2010/034,
      author = {Xiwang Cao},
      title = {On the order of the polynomial $x^p-x-a$},
      howpublished = {Cryptology ePrint Archive, Paper 2010/034},
      year = {2010},
      note = {\url{https://eprint.iacr.org/2010/034}},
      url = {https://eprint.iacr.org/2010/034}
}