Continued Fractions of Square Roots of Natural Numbers

L'ubomíra Balková, Aranka Hrušková

Abstract


In this paper, we will first summarize known results concerning continued fractions. Then we will limit our consideration to continued fractions of quadratic numbers. The second author describes periods and sometimes the precise form of continued fractions of ?N, where N is a natural number. In cases where we have been able to find such results in the literature, we recall the original authors, however many results seem to be new.

Keywords


continued fractions; periodic continued fractions; periods of continued fractions; quadratic numbers

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ISSN 1210-2709 (Print)
ISSN 1805-2363 (Online)
Published by the Czech Technical University in Prague