Open AccessSolving Diophantine Equations by Factoring in Number Fields
Author(s) -
Zdeněk Pezlar
Publication year - 2021
Publication title -
journal of the asb society
Language(s) - English
Resource type - Journals
ISSN - 2695-1010
DOI - 10.51337/jasb20211227004
Subject(s) - diophantine equation , factoring , algebraic number , number theory , algebraic number theory , diophantine set , mathematics , algebra over a field , algebraic equation , diophantine geometry , quadratic equation , computer science , discrete mathematics , pure mathematics , mathematical analysis , physics , geometry , finance , nonlinear system , quantum mechanics , economics
In this text we provide an introduction to algebraic number theory and show its applications in solving certain difficult diophantine equations. We begin with a quick summary of the theory of quadratic residues, before diving into a select few areas of algebraic number theory. Our article is accompanied by a couple of worked problems and exercises for the reader to tackle on their own.