<abstract xmlns="http://www.w3.org/1999/xhtml">In this article we formalize several basic theorems that correspond to Pell’s equation. We focus on two aspects: that the Pell’s equation <italic>x</italic>2 − <italic>Dy</italic>2 = 1 has infinitely many solutions in positive integers for a given <italic>D</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 <monospace>#39</monospace> from the “Formalizing 100 Theorems” list maintained by Freek Wiedijk at <ext-link ext-link-type="uri" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="http://www.cs.ru.nl/F.Wiedijk/100/">http://www.cs.ru.nl/F.Wiedijk/100/</ext-link>.</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/.

Pell’s Equation

Formalized Mathematics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Pell\u2019s Equation"}

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...

Pell’s Equation

Online veröffentlicht: 19. Dez. 2017

Seitenbereich: 197 - 204

Eingereicht: 30. Aug. 2017

DOI: https://doi.org/10.1515/forma-2017-0019

Schlüsselwörter
Pell’s equation, Diophantine equation, Hilbert’s 10th problem

© 2017 Marcin Acewicz et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Pell’s Equation

Online veröffentlicht: 19. Dez. 2017

Seitenbereich: 197 - 204

Eingereicht: 30. Aug. 2017

DOI: https://doi.org/10.1515/forma-2017-0019

SchlüsselwörterPell’s equation, Diophantine equation, Hilbert’s 10th problem

© 2017 Marcin Acewicz et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Schlüsselwörter
Pell’s equation, Diophantine equation, Hilbert’s 10th problem