Number Theory and Its History [NOOK Book]

Overview



A prominent mathematician presents the principal ideas and methods of number theory within a historical and cultural framework. Oystein Ore's fascinating, accessible treatment requires only a basic knowledge of algebra. Topics include prime numbers, the Aliquot parts, linear indeterminate problems, congruences, Euler's theorem, classical construction problems, and many other subjects.
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Number Theory and Its History

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Overview



A prominent mathematician presents the principal ideas and methods of number theory within a historical and cultural framework. Oystein Ore's fascinating, accessible treatment requires only a basic knowledge of algebra. Topics include prime numbers, the Aliquot parts, linear indeterminate problems, congruences, Euler's theorem, classical construction problems, and many other subjects.
Read More Show Less

Product Details

  • ISBN-13: 9780486136431
  • Publisher: Dover Publications
  • Publication date: 6/8/2012
  • Series: Dover Books on Mathematics
  • Sold by: Barnes & Noble
  • Format: eBook
  • Pages: 380
  • Sales rank: 526,644
  • File size: 13 MB
  • Note: This product may take a few minutes to download.

Table of Contents

Preface
Chapter 1. Counting and Recording of Numbers
1. Numbers and counting
2. Basic number groups
3. The number systems
4. Large numbers
5. Finger numbers
6. Recordings of numbers
7. Writing of numbers
8. Calculations
9. Positional numeral systems
10. Hindu-Arabic numerals
Chapter 2. Properties of Numbers. Division
1. Number theory and numerology
2. Multiples and divisors
3. Division and remainders
4. Number systems
5. Binary number systems
Chapter 3. Euclid's Algorism
1. Greatest common divisor. Euclid's algorism
2. The division lemma
3. Least common multiple
4. Greatest common divisor and least common multiple for several numbers
Chapter 4. Prime Numbers
1. Prime numbers and the prime factorization theorem
2. Determination of prime factors
3. Factor tables
4. Fermat's factorization method
5. Euler's factorization method
6. The sieve of Eratosthenes
7. Mersenne and Fermat primes
8. The distribution of primes
Chapter 5. The Aliquot Parts
1. The divisors of a number
2. Perfect numbers
3. Amicable numbers
4. Greatest common divisor and least common multiple
5. Euler's function
Chapter 6. Indeterminate Problems
1. Problems and puzzles
2. Indeterminate problems
3. Problems with two unknowns
4. Problems with several unknowns
Chapter 7. Theory of Linear Indeterminate Problems
1. Theory of linear indeterminate equations with two unknowns
2. Linear indeterminate equations in several unknowns
3. Classification of systems of numbers
Chapter 8. Diophantine Problems
1. The Pythagorean triangle
2. The Plimpton Library tablet
3. Diophantos of Alexandria
4. AI-Karkhi and Leonardo Pisano
5. From Diophantos to Fermat
6. The method of infinite descent
7. Fermat's last theorem
Chapter 9. Congruences
1. The Disquisitiones arithmeticae
2. The properties of congruences
3. Residue systems
4. Operations with congruences
5. Casting out nines
Chapter 10. Analysis of Congruences
1. Algebraic congruences
2. Linear congruences
3. Simultaneous congruences and the Chinese remainder theorem
4. Further study of algebraic congruences
Chapter 11. Wilson's Theorem and Its Consequences
1. Wilson's theorem
2. Gauss's generalization of Wilson's theorem
3. Representations of numbers as the sum of two squares
Chapter 12. Euler's Theorem and Its Consequences
1. Euler's theorem
2. Fermat's theorem
3. Exponents of numbers
4. Primitive roots for primes
5. "Primitive roots for powers of primes, "
6. Universal exponents
7. Indices
8. Number theory and the splicing of telephone cables
Chapter 13. Theory of Decimal Expansions
1. Decimal fractions
2. The properties of decimal fractions
Chapter 14. The Converse of Fermat's Theorem
1. The converse of Fermat's theorem
2. Numbers with the Fermat property
Chapter 15. The Classical Construction Problems
1. The classical construction problems
2. The construction of regular polygons
3. Examples of constructible polygons
Supplement
Bibliography
General Name Index
Subject Index
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