Convergence of the Brun algorithm over the field of formal power series (Q1011681)

Let \(\mathbb F_q\) be the field with \(q\) elements and \(\mathbb F_q((X^{-1}))\) the field of formal power series. The authors imitate the methods used in the real numbers case to define some kind of Brun algorithm over \(\mathbb F_q((X^{-1}))\) and to prove its convergence.