Zentralblatt MATH
Publications of (and about) Paul Erdös
Zbl.No: 747.11005
Autor: Erdös, Paul; Horváth, M.; Joó, I.
Title: On the uniqueness of the expansions 1 = sum q-ni. (In English)
Source: Acta Math. Hung. 58, No.3/4, 333-342 (1991).
Review: For a real number 1 < q < 2, consider the equation 1 = sum+oon = 1en/qn, where en = 0 or 1. The digits en can uniquely be determined only if an algorithm is given for the preceding expansion; see [J. Galambos, Representations of real numbers by infinite series (1976; Zbl 322.10002), pp. 3, 13 and 62]. Otherwise, for most q, there are infinitely many ways for obtaining the sequence en, n \geq 1. The paper is devoted to analyzing the structure and the size of the set {en, n \geq 1} in the absence of an algorithm.
Reviewer: J.Galambos (Philadelphia)
Classif.: * 11A67 Representation systems for integers and rationals
Keywords: power series representation; lack of algorithm; non-uniqueness
Citations: Zbl 322.10002
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