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Pell’s Equation

Published:2017-10-01 Issue:3 Volume:25 Page:197-204
ISSN:1898-9934
Container-title:Formalized Mathematics
language:en
Short-container-title:

Author:

Acewicz Marcin¹,Pąk Karol¹

Affiliation:

1. Institute of Informatics , University of Białystok , Poland

Abstract

Summary In this article we formalize several basic theorems that correspond to Pell’s equation. We focus on two aspects: that the Pell’s equation x 2 − Dy 2 = 1 has infinitely many solutions in positive integers for a given D 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 #39 from the “Formalizing 100 Theorems” list maintained by Freek Wiedijk at http://www.cs.ru.nl/F.Wiedijk/100/.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Computational Mathematics

Reference10 articles.

1. [1] Grzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, Karol Pąk, and Josef Urban. Mizar: State-of-the-art and beyond. In Manfred Kerber, Jacques Carette, Cezary Kaliszyk, Florian Rabe, and Volker Sorge, editors, Intelligent Computer Mathematics, volume 9150 of Lecture Notes in Computer Science, pages 261–279. Springer International Publishing, 2015. ISBN 978-3-319-20614-1. doi:10.1007/978-3-319-20615-8_17.10.1007/978-3-319-20615-8_17

2. [2] John Harrison. The HOL Light system REFERENCE. 2014. http://www.cl.cam.ac.uk/~jrh13/hol-light/reference.pdf.

3. [3] B. Krumbiegel and A. Amthor. Das Problema Bovinum des Archimedes. Historischliterarische Abteilung der Zeitschrift fur Mathematik und Physik, 25:121–136, 153–171, 1880.

4. [4] Joseph L. Lagrange. Solution d’un probleème d’arithmétique. Mélanges de philosophie et de math. de la Société Royale de Turin, (44–97), 1773.

5. [5] Hendrik W. Lenstra. Solving the Pell equation. Algorithmic Number Theory, 44:1–24, 2008.

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