Periodicity of \(p\)-adic continued fractions
\textit{Th. Schneider} [Symp. Math. 4, 181--189 (1970; Zbl 0222.10035)] defined continued fraction expansions for \(p\)-adic numbers. The author shows that contrary to the real case quadratic roots of rational integers lying in \(\mathbb Q_p\) may not have a periodic expansion. This happens in particular to all quadratic roots of negative numbers.
scientific article; zbMATH DE number 4148228