<abstract xmlns="http://www.w3.org/1999/xhtml"><p> In this article, we prove selected properties of Pell’s equation that are essential to finally prove the Diophantine property of two equations. These equations are explored in the proof of Matiyasevich’s negative solution of Hilbert’s tenth problem.</p></abstract>

In this article, we prove selected properties of Pell’s equation that are essential to finally prove the Diophantine property of two equations. These equations are explored in the proof of Matiyasevich’s negative solution of Hilbert’s tenth problem.

The Matiyasevich Theorem. Preliminaries

Formalized Mathematics

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International (CC BY-SA 4.0) License.

{"article-title":"The Matiyasevich Theorem. Preliminaries"}

In this article, we prove selected properties of Pell’s equation that are essential to finally prove the Diophantine property of two equations. These equations...

The Matiyasevich Theorem. Preliminaries

Published Online: Mar 28, 2018

Page range: 315 - 322

Received: Nov 29, 2017

DOI: https://doi.org/10.1515/forma-2017-0029

Keywords
Pell’s equation, Diophantine equation, Hilbert’s 10th problem

© by Karol Pak

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International (CC BY-SA 4.0) License.

The Matiyasevich Theorem. Preliminaries

Published Online: Mar 28, 2018

Page range: 315 - 322

Received: Nov 29, 2017

DOI: https://doi.org/10.1515/forma-2017-0029

KeywordsPell’s equation, Diophantine equation, Hilbert’s 10th problem

© by Karol Pak

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International (CC BY-SA 4.0) License.

Keywords
Pell’s equation, Diophantine equation, Hilbert’s 10th problem