# Elementary Methods in Number Theory

• Melvyn B. Nathanson
Book

Part of the Graduate Texts in Mathematics book series (GTM, volume 195)

1. Front Matter
Pages i-xviii
2. ### A First Course in Number Theory

1. Front Matter
Pages 1-1
2. Pages 3-43
3. Pages 45-81
4. Pages 83-120
5. Pages 121-169
6. Pages 171-197
3. ### Divisors and Primes in Multiplicative Number Theory

1. Front Matter
Pages 199-199
2. Pages 201-229
3. Pages 231-266
4. Pages 267-288
5. Pages 289-323
6. Pages 325-351
4. ### Three Problems in Additive Number Theory

1. Front Matter
Pages 353-353
2. Pages 355-374
3. Pages 375-399
4. Pages 401-421
5. Pages 423-454
6. Pages 455-474
7. Pages 475-495

### Introduction

Elementary Methods in Number Theory begins with "a first course in number theory" for students with no previous knowledge of the subject. The main topics are divisibility, prime numbers, and congruences. There is also an introduction to Fourier analysis on finite abelian groups, and a discussion on the abc conjecture and its consequences in elementary number theory. In the second and third parts of the book, deep results in number theory are proved using only elementary methods. Part II is about multiplicative number theory, and includes two of the most famous results in mathematics: the Erdös-Selberg elementary proof of the prime number theorem, and Dirichlets theorem on primes in arithmetic progressions. Part III is an introduction to three classical topics in additive number theory: Warings problems for polynomials, Liouvilles method to determine the number of representations of an integer as the sum of an even number of squares, and the asymptotics of partition functions. Melvyn B. Nathanson is Professor of Mathematics at the City University of New York (Lehman College and the Graduate Center). He is the author of the two other graduate texts: Additive Number Theory: The Classical Bases and Additive Number Theory: Inverse Problems and the Geometry of Sumsets.

### Keywords

Prime Prime number Waring's problem calculus number theory

#### Authors and affiliations

• Melvyn B. Nathanson
• 1
1. 1.Department of MathematicsLehman College (CUNY)BronxUSA

### Bibliographic information

• DOI https://doi.org/10.1007/b98870
• Copyright Information Melvyn B. Nathanson 2000
• Publisher Name Springer, New York, NY
• eBook Packages
• Print ISBN 978-0-387-98912-9
• Online ISBN 978-0-387-22738-2
• Series Print ISSN 0072-5285