Approximation by continued fractions
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- by Melvyn B. Nathanson PDF
- Proc. Amer. Math. Soc. 45 (1974), 323-324 Request permission
Abstract:
Let $x$ be a real irrational number whose continued fraction has infinitely many partial quotients not less than $k$. A simple proof is given that the inequality $|x - p/q| < (k^2 + 4)^{-1/2} q^{-2}$ has infinitely many rational solutions $p/q$. The constant $(k^2 + 4)^{-1/2}$ is best possible.References
- J. H. E. Cohn, Hurwitz’ theorem, Proc. Amer. Math. Soc. 38 (1973), 436. MR 313195, DOI 10.1090/S0002-9939-1973-0313195-9 G. H. Hardy and E. M. Wright, An introduction to the theory of numbers, 4th ed., Oxford Univ. Press, London, 1960.
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 45 (1974), 323-324
- MSC: Primary 10F20
- DOI: https://doi.org/10.1090/S0002-9939-1974-0349594-X
- MathSciNet review: 0349594