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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 

 

Continued fractions and linear recurrences


Authors: H. W. Lenstra and J. O. Shallit
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
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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.


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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1993-1192972-X
Keywords: Continued fractions, linear recurrences
Article copyright: © Copyright 1993 American Mathematical Society