# Pell’s Equation

Formalized Mathematics (2017)

- Volume: 25, Issue: 3, page 197-204
- ISSN: 1426-2630

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topMarcin 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 -

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