Consecutive powers in continued fractions
R. A. Mollin, H. C. Williams (1992)
Acta Arithmetica
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R. A. Mollin, H. C. Williams (1992)
Acta Arithmetica
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Mollin, Richard A. (2001)
International Journal of Mathematics and Mathematical Sciences
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Colţescu, Ion (2002)
Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică
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Mordechay Levin, Meir Smorodinsky (2000)
Colloquium Mathematicae
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We extend the Davenport and Erdős construction of normal numbers to the case.
Balamohan, B., Kuznetsov, A., Tanny, Stephen (2007)
Journal of Integer Sequences [electronic only]
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Lascoux, Alain (2000)
Séminaire Lotharingien de Combinatoire [electronic only]
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Brugia, Odoardo, Filipponi, Piero (2000)
International Journal of Mathematics and Mathematical Sciences
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Kudajbergenov, K.Zh. (2000)
Siberian Mathematical Journal
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Anatoly Zhigljavsky, Iskander Aliev (1999)
Acta Arithmetica
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Sen-Shan Huang (1997)
Acta Arithmetica
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Winkel, Rudolf (1996)
Séminaire Lotharingien de Combinatoire [electronic only]
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Guillaume Grisel (1998)
Acta Arithmetica
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Let d ≥ 2 be a square-free integer and for all n ≥ 0, let be the length of the continued fraction expansion of . If ℚ(√d) is a principal quadratic field, then under a condition on the fundamental unit of ℤ[√d] we prove that there exist constants C₁ and C₂ such that for all large n. This is a generalization of a theorem of S. Chowla and S. S. Pillai [2] and an improvement in a particular case of a theorem of [6].
R. A. Mollin (1998)
Acta Arithmetica
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The purpose of this paper is to generalize some seminal results in the literature concerning the interrelationships between Legendre symbols and continued fractions. We introduce the power of ideal theory into the arena. This allows significant improvements over the existing results via the infrastructure of real quadratic fields.