On continued fractions of given period
HTML articles powered by AMS MathViewer
- by Christian Friesen PDF
- Proc. Amer. Math. Soc. 103 (1988), 9-14 Request permission
Abstract:
A direct proof is given of the fact that, for any $k \in {{\mathbf {Z}}^ + }$, there are infinitely many squarefree integers $N$, where the continued fraction expansion of $\sqrt N$ has period equal to $k$.References
- P. Chowla and S. Chowla, Problems on periodic simple continued fractions, Proc. Nat. Acad. Sci. U.S.A. 69 (1972), 3745. MR 319942, DOI 10.1073/pnas.69.12.3745
- G. H. Hardy and E. M. Wright, An introduction to the theory of numbers, Oxford, at the Clarendon Press, 1954. 3rd ed. MR 0067125
- Oskar Perron, Die Lehre von den Kettenbrüchen, Chelsea Publishing Co., New York, N. Y., 1950 (German). 2d ed. MR 0037384
Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 103 (1988), 9-14
- MSC: Primary 11A55
- DOI: https://doi.org/10.1090/S0002-9939-1988-0938635-4
- MathSciNet review: 938635