Strong convergence of additive Multidimensional Continued Fraction algorithms
Kentaro Nakaishi (2006)
Acta Arithmetica
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Kentaro Nakaishi (2006)
Acta Arithmetica
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Yong-Gao Chen, Christian Elsholtz, Li-Li Jiang (2012)
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]. ...
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.
Dajani, Karma, Kraaikamp, Cor (1998)
The New York Journal of Mathematics [electronic only]
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Jincheng Tong (1992)
Mathematica Scandinavica
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Dominique Barbolosi, Hendrik Jager (1994)
Journal de théorie des nombres de Bordeaux
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Jeffrey C. Lagarias, Jeffrey O. Shallit (2003)
Journal de théorie des nombres de Bordeaux
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We fill a gap in the proof of a theorem of our paper cited in the title.
Takao Komatsu (2003)
Acta Arithmetica
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Boris Adamczewski (2010)
Acta Arithmetica
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Meignen, Pierrick (1999)
Beiträge zur Algebra und Geometrie
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James Mc Laughlin (2008)
Acta Arithmetica
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Florin P. Boca, Joseph Vandehey (2012)
Acta Arithmetica
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