de Weger, B. M. M. Periodicity of \(p\)-adic continued fractions. (English) Zbl 0701.11066 Elem. Math. 43, No. 4, 112-116 (1988). 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. Reviewer: Władysław Narkiewicz (Wrocław) Cited in 3 ReviewsCited in 14 Documents MSC: 11J70 Continued fractions and generalizations 11S85 Other nonanalytic theory 11A55 Continued fractions Keywords:quadratic irrationalities; continued fraction expansions; p-adic numbers; periodic expansion Citations:Zbl 0222.10035 PDFBibTeX XMLCite \textit{B. M. M. de Weger}, Elem. Math. 43, No. 4, 112--116 (1988; Zbl 0701.11066) Full Text: EuDML