Pell’s Equation

Marcin Acewicz, and Karol Pąk. "Pell’s Equation." Formalized Mathematics 25.3 (2017): 197-204. <http://eudml.org/doc/288558>.

@article{MarcinAcewicz2017,
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/.},
author = {Marcin Acewicz, Karol Pąk},
journal = {Formalized Mathematics},
keywords = {Pell’s equation; Diophantine equation; Hilbert’s 10th problem},
language = {eng},
number = {3},
pages = {197-204},
title = {Pell’s Equation},
url = {http://eudml.org/doc/288558},
volume = {25},
year = {2017},
}

TY - JOUR
AU - Marcin Acewicz
AU - Karol Pąk
TI - Pell’s Equation
JO - Formalized Mathematics
PY - 2017
VL - 25
IS - 3
SP - 197
EP - 204
AB - 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/.
LA - eng
KW - Pell’s equation; Diophantine equation; Hilbert’s 10th problem
UR - http://eudml.org/doc/288558
ER -