CryptoDB
On the order of the polynomial $x^p-x-a$
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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 $\mathbb{F}_p$. |
BibTeX
@misc{eprint-2010-22935, title={On the order of the polynomial $x^p-x-a$}, booktitle={IACR Eprint archive}, keywords={foundations /}, url={http://eprint.iacr.org/2010/034}, note={ xwcao@nuaa.edu.cn 14630 received 21 Jan 2010}, author={Xiwang Cao}, year=2010 }