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

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

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