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Pell’s Equation

Marcin Acewicz

Marcin Acewicz

Institute of Informatics, University of BiałystokPoland
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Acewicz, Marcin
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Karol Pąk

Karol Pąk

Institute of Informatics, University of BiałystokPoland
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Pąk, Karol
  
Dec 19, 2017
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Published Online: Dec 19, 2017
Page range: 197 - 204
Received: Aug 30, 2017
DOI: https://doi.org/10.1515/forma-2017-0019
Keywords
© 2017 Marcin Acewicz et al., published by De Gruyter Open
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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/.

Language:
English
Publication timeframe:
1 times per year
Journal Subjects:
Mathematics, General Mathematics, Computer Sciences, Computer Sciences, other
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