Pell’s Equation

• Autorzy: Marcin Acewicz , Karol Pąk
• Języki publikacji: EN

Abstrakty

EN

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/.

Słowa kluczowe

EN

Pell’s equation; Diophantine equation; Hilbert’s 10th problem

Kategorie tematyczne

• 03B35: Mechanization of proofs and logical operations
• 11D45: Counting solutions of Diophantine equations

• Wydawca: De Gruyter Open
• Czasopismo: Formalized Mathematics
• Rocznik: 2017
• Tom: 25
• Numer: 3
• Strony: 197-204

Daty

wydano

2017-10-01

otrzymano

2017-08-30

online

2017-12-19

Twórcy

autor

Marcin Acewicz

• , ,

autor

Karol Pąk

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Identyfikatory

DOI

10.1515/forma-2017-0019