Laohakosol, Vichian; Kanasri, Narakorn Rompurk A characterization of rational numbers by \(p\)-adic Sylvester series expansions. (English) Zbl 1140.11003 Acta Arith. 130, No. 4, 389-402 (2007). It is proved that a \(p\)-adic number is rational if and only if its \(p\)-adic Sylvester series expansion, defined via the Knopfmachers’ algorithm, is either finite or infinite of a particular shape. Note that the situation for fields of formal Laurent series over a finite field is much simpler (see a paper by the same authors and A. Harnchoowong [Thai J. Math. 4, 223–244 (2006)] Reviewer: Jean-Paul Allouche (Orsay) Cited in 1 Document MSC: 11A67 Other number representations 11J61 Approximation in non-Archimedean valuations Keywords:\(p\)-adic number; Sylvester series expansion; Knopfmachers’ algorithm PDFBibTeX XMLCite \textit{V. Laohakosol} and \textit{N. R. Kanasri}, Acta Arith. 130, No. 4, 389--402 (2007; Zbl 1140.11003) Full Text: DOI