@MISC{PELLS_EQ.MIZ,
  AUTHOR = {Acewicz, Marcin and P\k{a}k, Karol},
  TITLE = {The Pell's Equation},
  NOTE = {This work has been financed by the
    resources of the Polish National Science Centre granted by decision
    no. DEC-2015/19/D/ST6/01473.},
  SECTION1 = {Preliminaries},
  SECTION2 = {Solutions to Pell's Equation -- Construction},
  SECTION3 = {Pell's Equation},
  SECTION4 = {Solutions to Pell's Equation -- Shape},
  DAY = {30},
  MONTH = {August},
  YEAR = {2017},
  ADDRESS1 = {Institute of Informatics\\University of Bia{\l}ystok\\Konstantego Cio{\l}kowskiego 1M, 15-245 Bia{\l}ystok\\Poland},
  ADDRESS2 = {Institute of Informatics\\University of Bia{\l}ystok\\Konstantego Cio{\l}kowskiego 1M, 15-245 Bia{\l}ystok\\Poland},
  SUMMARY = {In this article we prove several basic theorems that correspond to the Pell's Equation.
  First we focus on the theorem that the Pell's equation $x^2-Dy^2 = 1$ has
  infinitely many solutions in positive integers for a given non square natural number $D$.
  We present also a formalization of a theorem that based on the least fundamental
  solution of the equation we can simply calculate algebraically each remaining solution.
  \par The formalization follows W. Sierpiński \cite{Sierpinski64}.
  Solutions to Pell's Equation are listed as \#39 at Freek Wiedijk's
  list of ``Top 100 mathematical theorems" \cite{Freek-100-theorems}.}}


@book{Sierpinski64,
  author =       {Sierpi\'nski, Wac³aw},
  editor = {Schinzel, A.},
  title =        {Elementary theory of numbers},
  publisher =    {Mathematical Institute of the Polish Academy of Science},
  year =         {1964}
}
