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

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Abstract

In this paper we prove some results on the possible multiplicative order 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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  1. Università degli Studi di Trento, Trento, Italy

    Simone Ugolini

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  1. Simone Ugolini
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Correspondence to Simone Ugolini.

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Ugolini, S. Some notes on the multiplicative order of \(\alpha + \alpha ^{-1}\) in finite fields of characteristic two. Period Math Hung 80, 81–94 (2020). https://doi.org/10.1007/s10998-019-00296-z

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