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arXiv · 1808.06527

Some notes on the multiplicative order of $\alpha + \alpha^{-1}$ in finite fields of characteristic two

Simone Ugolini
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Abstract

In this paper we prove some results on the possible multiplicative orders of $\alpha + \alpha^{-1}$ when $\alpha$ is a non-zero element of a finite field of characteristic 2. The results of the paper rely on a previous investigation on the structure of the graphs associated with the map $x \mapsto x + x^{-1}$ in finite fields of characteristic 2.

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Simone Ugolini. 2018-08-20. Some notes on the multiplicative order of $\alpha + \alpha^{-1}$ in finite fields of characteristic two. https://doi.org/10.1007/s10998-019-00296-z

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