Pell’s Equation

Marcin Acewicz; Karol Pąk

doi:10.1515/forma-2017-0019

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Pell’s Equation

Formalized Mathematics

Volume 25 (2017): Issue 3 (October 2017)

By: Marcin Acewicz and Karol Pąk

Open Access

|Dec 2017

Abstract

In this article we formalize several basic theorems that correspond to Pell’s equation. We focus on two aspects: that the Pell’s equation x² − Dy² = 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/.

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Articles in this issue

DOI: https://doi.org/10.1515/forma-2017-0019 | Journal eISSN: 1898-9934 | Journal ISSN: 1426-2630

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Language: English

Page range: 197 - 204

Submitted on: Aug 30, 2017

Published on: Dec 19, 2017

Published by: University of Białystok

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

Pell’s equation,

Diophantine equation,

Hilbert’s 10th problem

Related subjects:

Mathematics,

General mathematics,

Computer sciences,

Computer sciences, other

© 2017 Marcin Acewicz, Karol Pąk, published by University of Białystok
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 25 (2017): Issue 3 (October 2017)