Egyptian fractions with restrictions
Yong-Gao Chen, Christian Elsholtz, Li-Li Jiang (2012)
Acta Arithmetica
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Yong-Gao Chen, Christian Elsholtz, Li-Li Jiang (2012)
Acta Arithmetica
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Acu, Dumitru (1999)
General Mathematics
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Ryuta Hashimoto (2001)
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.
Meignen, Pierrick (1999)
Beiträge zur Algebra und Geometrie
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Maosheng Xiong, Alexandru Zaharescu (2006)
Acta Arithmetica
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Matthew Collins
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H. NAKADA (1987-1988)
Seminaire de Théorie des Nombres de Bordeaux
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Umberto Zannier (2003)
Acta Arithmetica
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Xiaolei Dong, W. C. Shiu, C. I. Chu, Zhenfu Cao (2007)
Acta Arithmetica
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P. Hubert, A. Messaoudi (2006)
Acta Arithmetica
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Utz, W.R. (1985)
International Journal of Mathematics and Mathematical Sciences
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Nikolai G. Moshchevitin (1999)
Journal de théorie des nombres de Bordeaux
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This paper is a brief review of some general Diophantine results, best approximations and their applications to the theory of uniform distribution.
Yasushige Watase (2015)
Formalized Mathematics
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In this article we formalize some results of Diophantine approximation, i.e. the approximation of an irrational number by rationals. A typical example is finding an integer solution (x, y) of the inequality |xθ − y| ≤ 1/x, where 0 is a real number. First, we formalize some lemmas about continued fractions. Then we prove that the inequality has infinitely many solutions by continued fractions. Finally, we formalize Dirichlet’s proof (1842) of existence of the solution [12], [1]. ...