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Introduction to Diophantine Approximation

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Watase Y.

Formalized Mathematics

2015

tom 23

nr 2

101-106

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].

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1 Formalized Mathematics

1 Watase Y.

1 2015

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Introduction to Diophantine Approximation