13 Lectures on Fermat's Last Theorem [Hardcover]

Lecture I The Early History of Fermats Last Theorem.- 1 The Problem.- 2 Early Attempts.- 3 Kummers Monumental Theorem.- 4 Regular Primes.- 5 Kummers Work on Irregular Prime Exponents.- 6 Other Relevant Results.- 7 The Golden Medal and the Wolfskehl Prize.- Lecture II Recent Results.- 1 Stating the Results.- 2 Explanations.- Lecture III B.K. = Before Kummer.- 1 The Pythagorean Equation.- 2 The Biquadratic Equation.- 3 The Cubic Equation.- 4 The Quintic Equation.- 5 Fermats Equation of Degree Seven.- Lecture IV The Na?ve Approach.- 1 The Relations of Barlow and Abel.- 2 Sophie Germain.- 3 Congruences.- 4 Wendts Theorem.- 5 Abels Conjecture.- 6 Fermats Equation with Even Exponent.- 7 Odds and Ends.- Lecture V Kummers Monument.- 1 A Justification of Kummers Method.- 2 Basic Facts about the Arithmetic of Cyclotomic Fields.- 3 Kummers Main Theorem.- Lecture VI Regular Primes.- 1 The Class Number of Cyclotomic Fields.- 2 Bernoulli Numbers and Kummers Regularity Criterion.- 3 Various Arithmetic Properties of Bernoulli Numbers.- 4 The Abundance of Irregular Primes.- 5 Computation of Irregular Primes.- Lecture VII Kummer Exits.- 1 The Periods of the Cyclotomic Equation.- 2 The Jacobi Cyclotomic Function.- 3 On the Generation of the Class Group of the Cyclotomic Field.- 4 Kummers Congruences.- 5 Kummers Theorem for a Class of Irregular Primes.- 6 Computations of the Class Number.- Lecture VIII After Kummer, a New Light.- 1 The Congruences of Mirimanoff.- 2 The Theorem of Krasner.- 3 The Theorems of Wieferich and Mirimanoff.- 4 Fermats Theorem and the Mersenne Primes.- 5 Summation Criteria.- 6 Fermat Quotient Criteria.- Lecture IX The Power of Class Field Theory.- 1 The Power Residue Symbol.- 2 Kummer Extensions.- 3 The Main Theorems of Furtw?ngler.- 4 The Method of Singular Integers.- 5 Hasse.- 6 The p-Rank of the Class Group of the Cyclotomic Field.- 7 Criteria of p-Divisibility of the Class Number.- 8 Properly and Improperly Irregular Cyclotomic Fields.- Lecturlól