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/.

Język:: Angielski

Częstotliwość wydawania:: 1 razy w roku
Dziedziny czasopisma:: Matematyka, Matematyka ogólna, Informatyka, Informatyka, inne

Kanał RSS czasopisma

Pell’s Equation

Marcin Acewicz

Karol Pąk

Data publikacji: 19 gru 2017

Zakres stron: 197 - 204

Otrzymano: 30 sie 2017

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

Słowa kluczowePell’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.

Słowa kluczowe
Pell’s equation, Diophantine equation, Hilbert’s 10th problem