@MISC{DIOPHAN1.MIZ,
  AUTHOR = {Watase, Yasushige},
  TITLE = {Introduction to {D}iophantine Approximation},
  SECTION1 = {Irrational Numbers and Continued Fractions},
  SECTION2 = {Integer Solution of $| x\theta - y | \leq 1/x$},
  SECTION3 = {Proof of Dirichlet's Theorem},
  DAY = {19},
  MONTH = {April},
  YEAR = {2015},
  ADDRESS1 = {Suginami-ku Matsunoki 6, 3-21 Tokyo\\Japan},
  SUMMARY = {This article provides a formalized proof of known
  results of approximation of an irrational by rational numbers.
  A typical example of Diophantine approximation is to find integer
  solution $(x,y)$ of the inequality $| x\theta - y | \leq  1/x$
  where $\theta$ is a real. Firstly we provide necessary results from
  continued fractions. Secondary we prove the inequality has infinitely
  many solution by a continued fraction. Finally provided Dirichlet's
  proof (1842) of existence of the solution \cite{HardyWright:2008},
  \cite{Baker:1984}.}}

@BOOK{HardyWright:2008,
 AUTHOR={G. H. Hardy and E. M. Wright},
 TITLE={An Introduction to The Theory of Numbers 6th edition},
 PUBLISHER={Oxford University Press},
 YEAR=2008}

@BOOK{Baker:1984,
 AUTHOR={Baker, Alan},
 TITLE={A Concise Introduction to The Theory of Numbers},
 PUBLISHER={Cambridge University Press},
 YEAR=1984}
