Pell’s 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 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/.

Lingua:: Inglese

Frequenza di pubblicazione:: 1 volte all'anno
Argomenti della rivista:: Matematica, Matematica generale, Informatica, Informatica, altro

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Pell’s Equation

Marcin Acewicz

Karol Pąk

Pubblicato online: 19 dic 2017

Pagine: 197 - 204

Ricevuto: 30 ago 2017

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

Parole chiavePell’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.

Parole chiave
Pell’s equation, Diophantine equation, Hilbert’s 10th problem