Continued fractions and linear recurrences
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- by H. W. Lenstra and J. O. Shallit PDF
- Math. Comp. 61 (1993), 351-354 Request permission
Abstract:
We prove that the numerators and denominators of the convergents to a real irrational number $\theta$ satisfy a linear recurrence with constant coefficients if and only if $\theta$ is a quadratic irrational. The proof uses the Hadamard Quotient Theorem of A. van der Poorten.References
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Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Math. Comp. 61 (1993), 351-354
- MSC: Primary 11A55; Secondary 11B37
- DOI: https://doi.org/10.1090/S0025-5718-1993-1192972-X
- MathSciNet review: 1192972