On Robbins' example of a continued fraction expansion for a quartic power series over \(\mathbb F_{13}\) (Q2483155)

The author considers the continued fraction expansion for a quartic power series over the finite field. This expansion over the field \(\mathbb{F}_{13}\) was conjectured by Mills, Robbins and Buck [see \textit{W. H. Mills} and \textit{D. P. Robbins}, ``Continued fractions for certain algebraic power series'', J. Number Theory 23, 388--404 (1986; Zbl 0591.10021) and \textit{M. W. Buck} and \textit{D. P. Robbins}, ``The continued fraction of an algebraic power series satisfying a quartic equation'', J. Number Theory 50, No. 2, 335--344 (1995; Zbl 0822.11051)]. In the presented paper, the author proves this conjecture by describing the continued fraction expansion for a large family of algebraic power series over a finite field.