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Proceedings of the American Mathematical Society

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On continued fractions of given period

Author: Christian Friesen
Journal: Proc. Amer. Math. Soc. 103 (1988), 9-14
MSC: Primary 11A55
MathSciNet review: 938635
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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 [Enhancements On Off] (What's this?)

  • [1] P. Chowla and S. Chowla, Problems on periodic simple continued fractions, Proc. Nat. Acad. Sci. U.S.A. 69 (1972), 37-45. MR 0319942 (47:8483)
  • [2] G. H. Hardy and E. M. Wright, An introduction to the theory of numbers, 3rd ed., Clarendon Press, Oxford, 1954. MR 0067125 (16:673c)
  • [3] Oskar Perron, Die Lehre von den Kettenbruechen, Chelsea, New York, 1950. MR 0037384 (12:254b)

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Article copyright: © Copyright 1988 American Mathematical Society

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