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Remarks on continued fractions with finitely many digits

Volume 203 / 2022

Fritz Schweiger Acta Arithmetica 203 (2022), 239-250 MSC: 11A63, 11K55, 28D05, 37A44. DOI: 10.4064/aa210616-7-1 Published online: 5 May 2022

Abstract

It is shown that for any even number $N \geq 4$ there exists a continued fraction with finitely many digits and full cylinders. If $N \geq 3$ is odd, no continued fraction with finitely many digits and full cylinders exists. Furthermore, some more general configurations are discussed.

Authors

  • Fritz SchweigerFB Mathematik
    Universität Salzburg
    Hellbrunnerstr. 34
    5020 Salzburg, Austria
    e-mail

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