## Cryptology ePrint Archive: Report 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 $\mathbb{F}_p$.

**Category / Keywords: **foundations /

**Date: **received 21 Jan 2010

**Contact author: **xwcao at nuaa edu cn

**Available format(s): **PDF | BibTeX Citation

**Version: **20100122:040630 (All versions of this report)

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