The Solution of Equations in Integers

by Gelfond, A. O.; Roberts, J. B.

• ISBN13: 9780486824598
• ISBN10: 0486824594
• Format: Paperback
• Copyright: 2018-04-18
• Publisher: Dover Publications

Summary

From Pythagoras to Fermat, Euler, and latter-day thinkers, mathematicians have puzzled over the determination of integral solutions of algebraic equations with integral coefficients and with more than one unknown. This text by A. O. Gelfond, an internationally renowned leader in the study of this area, offers a relatively elementary exploration of one of the most challenging problems in number theory.
Since equations in integers are encountered in issues related to physics and engineering, the solution of these equations is a matter of practical applications. Nevertheless, the theoretical interest in equations in integers is also worth pursuing because these equations are closely connected with many problems in number theory. This volume's coverage of basic theoretical aspects of such equations promises to widen the horizons of readers from advanced high school students to undergraduate majors in mathematics, physics, and engineering.

Author Biography

A. O. Gelfond (1906–1968) was a prominent Soviet mathematician who was on the faculty of Moscow State University. Dover also publishes his Transcendental and Algebraic Numbers.
J. B. Roberts is Professor Emeritus of Mathematics at Reed College.

Table of Contents

Foreword

Preface

Introduction

1. Equations in One Unknown

2. Equations of the First Degree in Two Unknowns

3. Examples of Equations of Second Degree in Three Unknowns

4. Finding All Solutions of Equations of the Form x2 - Ay2 = 1

5. The General Case of Equations of Second Degree with Two Unknowns

6. Equations in Two Unknowns of Degree Higher Than the Second

7. Algebraic Equations of Degree Higher Than the Second with Three Unknowns and an Exponential Equation

Index