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ON A PROBLEM OF ERDÖS AND MAHLER CONCERNING CONTINUED FRACTIONS
Published online by Cambridge University Press: 19 October 2016
Abstract
In 1939, Erdös and Mahler [‘Some arithmetical properties of the convergents of a continued fraction’, J. Lond. Math. Soc. (2)14 (1939), 12–18] studied some arithmetical properties of the convergents of a continued fraction. In particular, they raised a conjecture related to continued fractions and Liouville numbers. In this paper, we shall apply the theory of linear forms in logarithms to obtain a result in the direction of this problem.
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- © 2016 Australian Mathematical Publishing Association Inc.