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

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.

13 pages; one graph added; presentation slightly revised; minor fixes

References in corpus (1)

• Graphs associated with the map $x\mapsto x+x^{-1}$ in finite fields of characteristic two