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Periodicity of \(p\)-adic continued fractions. (English) Zbl 0701.11066

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.

MSC:

11J70 Continued fractions and generalizations
11S85 Other nonanalytic theory
11A55 Continued fractions

Citations:

Zbl 0222.10035
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