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Continuum cardinality of the set of solutions of one class of equations that contain the function of frequency of ternary digits of a number

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Ukrainian Mathematical Journal Aims and scope

We study the equation ν 1(x) = x, where ν 1(x) is the function of frequency of the digit 1 in the ternary expansion of x. We prove that this equation has a unique rational root and a continuum set of irrational solutions. An algorithm for the construction of solutions is proposed. We also describe the topological and metric properties of the set of all solutions. Some additional facts about the equations ν i (x) = x, i = 0, 2, are given.

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Authors and Affiliations

  1. Kyiv National Pedagogic University, Kyiv, Ukraine

    O. V. Kotova

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  1. O. V. Kotova
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 10, pp. 1414–1421, October, 2008.

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Kotova, O.V. Continuum cardinality of the set of solutions of one class of equations that contain the function of frequency of ternary digits of a number. Ukr Math J 60, 1650–1659 (2008). https://doi.org/10.1007/s11253-009-0153-9

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  • DOI: https://doi.org/10.1007/s11253-009-0153-9

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