Pell's Equation release_jv4wi26vzjgofde5cgguvrjwgy

by Marcin Acewicz, Karol Pąk

Published in Formalized Mathematics by Walter de Gruyter GmbH.

2017   Volume 25, p197-204

Abstract

<jats:title>Summary</jats:title> In this article we formalize several basic theorems that correspond to Pell's equation. We focus on two aspects: that the Pell's equation <jats:italic>x</jats:italic><jats:sup>2</jats:sup> − <jats:italic>Dy</jats:italic><jats:sup>2</jats:sup> = 1 has infinitely many solutions in positive integers for a given <jats:italic>D</jats:italic> not being a perfect square, and that based on the least fundamental solution of the equation when we can simply calculate algebraically each remaining solution. "Solutions to Pell's Equation" are listed as item <jats:monospace>#39</jats:monospace> from the "Formalizing 100 Theorems" list maintained by Freek Wiedijk at <jats:ext-link xmlns:xlink="http://www.w3.org/1999/xlink" ext-link-type="uri" xlink:href="http://www.cs.ru.nl/F.Wiedijk/100/">http://www.cs.ru.nl/F.Wiedijk/100/</jats:ext-link>.
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