Lengths of periods of continued fractions of square roots of integers |
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Authors: | Vladimir I. Arnold |
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Affiliation: | 1. Steklov Mathematical Institute, 8 Gubkina St., Moscow, 119991, Russia
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Abstract: | Empirical study of the period’s length T of the continued fractions of $sqrt{Q}$ (for growing integers Q) shows several strange asymptotical results, for instance, $Tleq Csqrt{Q}ln{Q}$ . These results show important differences between the statistics of the elements of the continued fractions of random real numbers and of square roots of random integers. |
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