Displaying similar documents to “Arithmetic diophantine approximation for continued fractions-like maps on the interval”

Introduction to Diophantine Approximation

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]. ...

On the diophantine equation x²+x+1 = yz

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.