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Irrationality and transcendence of infinite continued fractions of square roots

Volume 184 / 2018

Jaroslav Hančl, Ondřej Kolouch, Radhakrishnan Nair Acta Arithmetica 184 (2018), 31-36 MSC: Primary 11J72. DOI: 10.4064/aa170221-21-9 Published online: 14 May 2018

Abstract

We give conditions on a sequence $\{a_n\}_{n=1}^\infty$ of positive integers sufficient to ensure that the number defined by the continued fraction expansion $[0;\sqrt{a_1},\sqrt{a_2},\dots ]$ is either irrational or transcendental.

Authors

  • Jaroslav HančlDepartment of Mathematics
    Faculty of Science
    University of Ostrava
    30. dubna 22
    701 03 Ostrava 1, Czech Republic
    e-mail
  • Ondřej KolouchDepartment of Mathematics
    Faculty of Science
    University of Ostrava
    30. dubna 22
    701 03 Ostrava 1, Czech Republic
    e-mail
  • Radhakrishnan NairMathematical Sciences
    University of Liverpool
    Peach Street
    Liverpool L69 7ZL, United Kingdom
    e-mail

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