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Number Theory Through the Eyes of Sophie Germain by Pengelley, David; is a book available to read on EtoBox.

What is Number Theory Through the Eyes of Sophie Germain about?

Cover 1 1/2 title page 2 Title page 4 Copyright page 5 Dedication 6 Contents 8 Preface 10 Chapter 1. Introduction 14 1.1. One theme, one unique researcher, and discovery detectives 15 1.2. How to use this book 16 1.3. Number theory cookies 17 Chapter 2. Sophie Germain, Number Theory, and Fermat’s Last Theorem 20 2.1. Sophie Germain, hidden mathematician 20 2.2. Number theory, queen of mathematics 23 2.3. Fermat’s last theorem, puzzle of centuries 30 Chapter 3. Germain’s Plan to Prove Fermat’s Last Theorem 34 3.1. The practice of being a detective 34 3.2. Residues 39 3.3. Primes in arithmetic progressions 42 3.4. Power residues 45 3.5. Consecutivity of power residues 48 Chapter 4. Fermat’s Last Theorem for Exponent Four 58 4.1. Pythagorean triples 58 4.2. Uniqueness of prime factorization 64 4.3. Euler’s proof for exponent four 64 4.4. Proofs of Euclid’s lemma on prime divisibility 71 4.4.1. Fermat’s method of descent revisited 71 4.4.2. The Euclidean algorithm and Bézout equation 72 4.4.3. How did Euclid (try to) prove his lemma? 76 4.4.4. Integral linear combinations 81 4.5. Divisibility, powers, roots, and equivalences 82 Chapter 5. Germain’s Grand Plan and a Letter to Gauss 84 5

Author

Pengelley, David;

Language

EN