Elementary Number Theory; Second Edition

by Dudley, Underwood

• ISBN13: 9780486469317
• ISBN10: 048646931X
• Edition: 2nd
• Format: Paperback
• Copyright: 2008-09-25
• Publisher: Dover Publications

Summary

Minimal prerequisites make this text ideal for a first course in number theory. Written in a lively, engaging style by the author of popular mathematics books, it features nearly 1,000 imaginative exercises and problems. Solutions to many of the problems are included, and a teacher's guide is available. 1978 edition.

Author Biography

Underwood Dudley is Professor Emeritus of Mathematics at DePauw University.

Underwood Dudley: Cranking Out Classics

Any editor involved with publishing in mathematics for any length of time is familiar with the phenomena — the receipt, usually via snail mail, of generally handwritten, and generally interminable, really, really interminable, theses on some bizarre and unprovable point — theses hoping, trying against all hope, demanding in fact, to prove the unprovable, to rewrite some fundamental part of mathematics, often in my experience to demonstrate for one final time that, for example, Einstein didn't know what he was talking about — in short, the work of a mathematical crank!

Underwood Dudley (Woody to everyone in the math world), Professor Emeritus, Depauw University, provided an inestimable service to all math editors in the universe by demonstrating that they are not alone in their experience. His unique and wonderful book Mathematical Cranks (The Mathematics Association of America, 1992) is a readable feast, especially for those who have been on the receiving end of mathematical crank mail. We're all in Woody's debt for having assembled this collection of failed squared circles, angle trisections, and much, much more.

However, chronicling the cranks — as enjoyable as it may have been to the rest of us — is hardly a career, Woody has written many other books as well. And any reader who wants to check out a totally uncranky, reader- and student-friendly, time-tested basic text in Elementary Number Theory could hardly do better than to look at the Dover edition of Woody's book by that name, which started its career with Freeman in 1969 and which Dover was pleased to reprint in 2008.

Table of Contents

Preface

Integers

Unique Factorization

Linear Diophantine Equations

Congruences

Linear Congruences

Fermat's and Wilson's Theorems

The Divisors of an Integer

Perfect Numbers

Euler's Theorem and Function

Primitive Roots

Quadratic Congruences

Quadratic Reciprocity

Numbers of Other Bases

Duodecimals

Decimals

Pythagorean Triangles

Infinite Descent and Fermat's Conjecture

Sums of Two Squares

Sums of Four Squares

x(superscript 2) - Ny(superscript 2) = 1

Bounds for pi(x)

Formulas for Primes

Additional problems

Proof by Induction

Computer Problems

Factor Table for Integers Less Than 10,000

References

Answers to Selected Exercises

Answers to Selected Odd-Numbered Problems

Comments on Selected Odd-Numbered Problems

Index