On two problems of Erdös Szüsz and Turan concerning diophantine approximations
Harry Kesten, V. Sós (1966)
Acta Arithmetica
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Harry Kesten, V. Sós (1966)
Acta Arithmetica
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Yong-Gao Chen, Christian Elsholtz, Li-Li Jiang (2012)
Acta Arithmetica
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A. Schinzel (2015)
Colloquium Mathematicae
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All solutions of the equation x²+x+1 = yz in non-negative integers x,y,z are given in terms of an arithmetic continued fraction.
Acu, Dumitru (1999)
General Mathematics
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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.
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.
Ryuta Hashimoto (2001)
Acta Arithmetica
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O'Bryant, Kevin (2003)
Integers
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Szalay, László (2007)
Annales Mathematicae et Informaticae
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Christoph Baxa (2000)
Mathematica Slovaca
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Makoto Nagata (2003)
Acta Arithmetica
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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]. ...