Elementary Number Theory

Philip Morrison, Underwood Dudley

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English

Dover
25 September 2008

Mathematics & Sciences; Number theory

Series: Dover Books on Mathema 1.4tics

Ideal for a first course in number theory, this lively, engaging text requires only a familiarity with elementary algebra and the properties of real numbers. Author Underwood Dudley, who has written a series of popular mathematics books, maintains that the best way to learn mathematics is by solving problems. In keeping with this philosophy, the text includes nearly 1,000 exercises and problems-some computational and some classical, many original, and some with complete solutions. The opening chapters offer sound explanations of the basics of elementary number theory and develop the fundamental properties of integers and congruences. Subsequent chapters present proofs of Fermat's and Wilson's theorems, introduce number theoretic functions, and explore the quadratic reciprocity theorem. Three independent sections follow, with examinations of the representation of numbers, diophantine equations, and primes. The text concludes with 260 additional problems, three helpful appendixes, and answers to selected exercises and problems.

By: Philip Morrison, Underwood Dudley
Imprint: Dover
Country of Publication: United States
Edition: 2nd
Dimensions: Height: 215mm, Width: 136mm, Spine: 12mm
Weight: 293g
ISBN: 9780486469317
ISBN 10: 048646931X
Series: Dover Books on Mathema 1.4tics
Pages: 249
Publication Date: 25 September 2008
Audience: General/trade , ELT Advanced
Format: Paperback
Publisher's Status: Unspecified

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

Reviews for Elementary Number Theory

Thompson and Lotze are to be commended for compiling this comprehensive work...The editors and authors should be commended for this very difficult task in this rapidly advancing field. There are excellent chapters on cytokine genetics, chemokine nomenclature, and the basic biology of each of the cytokines. -ASM NEWS (April 2004)