On Legendre's theorem related to diophantine approximations
S. ITO (1987-1988)
Seminaire de Théorie des Nombres de Bordeaux
Similarity:
S. ITO (1987-1988)
Seminaire de Théorie des Nombres de Bordeaux
Similarity:
Yong-Gao Chen, Christian Elsholtz, Li-Li Jiang (2012)
Acta Arithmetica
Similarity:
Kunrui YU (1980-1981)
Seminaire de Théorie des Nombres de Bordeaux
Similarity:
Acu, Dumitru (1999)
General Mathematics
Similarity:
A. Schinzel (2015)
Colloquium Mathematicae
Similarity:
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.
Yasushige Watase (2015)
Formalized Mathematics
Similarity:
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]. ...
Meignen, Pierrick (1999)
Beiträge zur Algebra und Geometrie
Similarity:
Avraham Bourla (2014)
Acta Arithmetica
Similarity:
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.
Maosheng Xiong, Alexandru Zaharescu (2006)
Acta Arithmetica
Similarity:
M. DODSON (1987-1988)
Seminaire de Théorie des Nombres de Bordeaux
Similarity:
Shunji ITO (1984-1985)
Seminaire de Théorie des Nombres de Bordeaux
Similarity:
Kentaro Nakaishi (2006)
Acta Arithmetica
Similarity:
Ryuta Hashimoto (2001)
Acta Arithmetica
Similarity: