- Browse
- » Number theory: a historical approach
Number theory: a historical approach
Author
Publisher
Princeton University Press
Publication Date
[2014]
Language
English
Description
Loading Description...
Table of Contents
From the Book
Machine generated contents note: 1.Number Theory Begins Pierre de Fermat Pythagorean Triangles Babylonian Mathematics Sexagesimal Numbers Regular Numbers Square Numbers Primitive Pythagorean Triples Infinite Descent Arithmetic Progressions Fibonacci's Approach Problems 2.Euclid Greek Mathematics Triangular Numbers Tetrahedral and Pyramidal Numbers The Axiomatic Method Proof by Contradiction Euclid's Self-Evident Truths Unique Factorization Pythagorean Tuning Problems 3.Divisibility The Euclidean Algorithm The Greatest Common Divisor The Division Algorithm Divisibility The Fundamental Theorem of Arithmetic Congruences Divisibility Tests Continued Fractions Problems 4.Diophantus The Arithmetica Problems from the Arithmetica A Note in the Margin Diophantine Equations Pell's Equation Continued Fractions Problems 5.Fermat Christmas Day, 1640
Contents note continued: Fermat's Little Theorem Primes as Sums of Two Squares Sums of Two Squares Perfect Numbers Mersenne Primes Fermat Numbers Binomial Coefficients "Multi Pertransibunt et Augebitur Scientia" Problems 6.Congruences Fermat's Little Theorem Linear Congruences Inverses The Chinese Remainder Theorem Wilson's Theorem Two Quadratic Congruences Lagrange's Theorem Problems 7.Euler and Lagrange A New Beginning Euler's Phi Function Primitive Roots Euler's Identity Quadratic Residues Lagrange Lagrange's Four Squares Theorem Sums of Three Squares Waring's Problem Fermat's Last Theorem Problems 8.Gauss The Young Gauss Quadratic Residues The Legendre Symbol Euler's Criterion Gauss's Lemma Euler's Conjecture The Law of Quadratic Reciprocity Problems 9.Primes I Factoring The Quadratic Sieve Method Is n Prime? Pseudoprimes Absolute Pseudoprimes
Contents note continued: A Probabilistic Test Can n Divide 2n1 or 2n+1? Mersenne Primes Problems 10.Primes II Gaps Both Large and Small The Twin Prime Conjecture The Series Bertrand's Postulate Goldbach's Conjecture Arithmetic Progressions Problems 11.Sophie Germain Monsieur LeBlanc Germain Primes Germain's Grand Plan Fermat's Last Theorem Problems 12.Fibonacci Numbers Fibonacci The Fibonacci Sequence The Golden Ratio Fibonacci Numbers in Nature Binet's Formula Tiling and the Fibonacci Numbers Fibonacci Numbers and Divisibility Generating Functions Problems 13.Cryptography Secret Codes on Mount Everest Caesar and Vigenere Ciphers Unbreakable Ciphers Public-Key Systems Problems 14.Continued Fractions The Golden Ratio Revisited Finite Continued Fractions Infinite Continued Fractions Approximation Pell's Equation Problems 15.Partitions Euler
Contents note continued: Generating Functions
Euler's Pentagonal Number Theorem
Ferrers Graphs
Ramanujan
Problems
Hints for Selected Problems
Solutions to Selected Problems
Brief Introduction to Sage
Suggestions for Further Reading
Pronunciation Guide
Table of Primes.
Excerpt
Loading Excerpt...
Author Notes
Loading Author Notes...
More Details
ISBN
9780691159409
Staff View
Loading Staff View.

