Invitation to number theory / by Oystein Ore.

Format:

Book

Author/Creator:

Ore, ystein, 1899-1968.

Series:

Anneli Lax New Mathematical Library ; no. 20

Language:

English

Subjects (All):

Number theory.

Algebra.

Physical Description:

1 online resource (viii, 129 pages) : digital, PDF file(s).

Edition:

1st ed.

Place of Publication:

Washington, D.C. : Mathematical Association of America, 1967.

Language Note:

English

Summary:

Number theory has been instrumental in introducing many of the most distinguished mathematicians, past and present, to the charms and mysteries of mathematical research. The purpose of this simple little guide will have been achieved if it should lead some of its readers to appreciate why the properties of numbers can be so fascinating. It would be better still if it would induce you to try to find some number relations of your own; new curiosities devised by young people turn up every year. In any case, you will become familiar with some of the special mathematical concepts and methods used in number theory and will be prepared to embark upon the study of the more advanced books in its rich literature.

Contents:

Front Cover

Invitation to Number Theory

Copyright Page

Contents

Chapter 1. Introduction

1.1 History

1.2 Numerology

1.3 The Pythagorean problem

1.4 Figurate numbers

1.5 Magic squares

Chapter 2. Primes

2.1 Primes and composite numbers

2.2 Mersenne primes

2.3 Fermat primes

2.4 The sieve of Eratosthenes

Chapter 3. Divisors of Numbers

3.1 Fundamental factorization theorem

3.2 Divisors

3.3 Problems concerning divisors

3.4 Perfect numbers

3.5 Amicable numbers

Chapter 4. Greatest Common Divisor and Least Common Multiple

4.1 Greatest common divisor

4.2 Relatively prime numbers

4.3 Euclid's algorithm

4.4 Least common multiple

Chapter 5. The Pythagorean Problem

5.1 Preliminaries

5.2 Solutions of the Pythagorean equation

5.3 Problems connected with Pythagorean triangles

Chapter 6. Numeration Systems

6.1 Numbers for the millions

6.2 Other systems

6.3 Comparison of numeration systems

6.4 Some problems concerning numeration systems

6.5 Computers and their numeration systems

6.6 Games with digits

Chapter 7. Congruences

7.1 Definition of congruence

7.2 Some properties of congruences

7.3 The algebra of congruences

7.4 Powers of congruences

7.5 Fermat's congruence

Chapter 8. Some Applications of Congruences

8.1 Checks on computations

8.2 The days of the week

8.3 Tournament schedules

8.4 Prime or composite?

Solutions to Selected Problems

References

Index.

Notes:

Title from publisher's bibliographic system (viewed on 02 Oct 2015).

Includes bibliographical references and index.

ISBN:

0-88385-960-2

OCLC:

929120428