Natural numbers n for which ⌊nα + s⌋ ≠ ⌊nβ + s⌋
Douglas Bowman, Alexandru Zaharescu (2012)
Acta Arithmetica
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Douglas Bowman, Alexandru Zaharescu (2012)
Acta Arithmetica
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Karl Dilcher, Kenneth B. Stolarsky (2009)
Acta Arithmetica
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Matveev, Andrey O. (2008)
Integers
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Jincheng Tong (1992)
Mathematica Scandinavica
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Filippo Mignosi, Luca Q. Zamboni (2002)
Acta Arithmetica
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Zongduo Dai, Ping Wang, Kunpeng Wang, Xiutao Feng (2007)
Acta Arithmetica
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Xue Hai Hu, Jun Wu (2009)
Acta Arithmetica
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Sebe, Gabriela Ileana (2002)
APPS. Applied Sciences
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D. Crisp, W. Moran, A. Pollington, P. Shiue (1993)
Journal de théorie des nombres de Bordeaux
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Marcel G. de-Bruin (1990)
Banach Center Publications
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Dominique Barbolosi, Hendrik Jager (1994)
Journal de théorie des nombres de Bordeaux
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Yan-Hui Qu, Hui Rao, Ya-Min Yang (2005)
Acta Arithmetica
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Avraham Bourla (2014)
Acta Arithmetica
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We establish arithmetical properties and provide essential bounds for bi-sequences of approximation coefficients associated with the natural extension of maps, leading to continued fraction-like expansions. These maps are realized as the fractional part of Möbius transformations which carry the end points of the unit interval to zero and infinity, extending the classical regular and backwards continued fraction expansions.
Florin P. Boca, Joseph Vandehey (2012)
Acta Arithmetica
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Boris Adamczewski, Yann Bugeaud (2007)
Annales de l’institut Fourier
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In the present work, we investigate real numbers whose sequence of partial quotients enjoys some combinatorial properties involving the notion of palindrome. We provide three new transendence criteria, that apply to a broad class of continued fraction expansions, including expansions with unbounded partial quotients. Their proofs heavily depend on the Schmidt Subspace Theorem.