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OverviewFull Product DetailsAuthor: Paulo RibenboimPublisher: Springer-Verlag New York Inc. Imprint: Springer-Verlag New York Inc. Edition: 1979 ed. Dimensions: Width: 15.60cm , Height: 1.90cm , Length: 23.40cm Weight: 1.420kg ISBN: 9780387904320ISBN 10: 0387904328 Pages: 302 Publication Date: 18 December 1979 Audience: College/higher education , General/trade , Postgraduate, Research & Scholarly , General Format: Hardback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsLecture I The Early History of Fermat’s Last Theorem.- 1 The Problem.- 2 Early Attempts.- 3 Kummer’s Monumental Theorem.- 4 Regular Primes.- 5 Kummer’s 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 Fermat’s Equation of Degree Seven.- Lecture IV The Naïve Approach.- 1 The Relations of Barlow and Abel.- 2 Sophie Germain.- 3 Congruences.- 4 Wendt’s Theorem.- 5 Abel’s Conjecture.- 6 Fermat’s Equation with Even Exponent.- 7 Odds and Ends.- Lecture V Kummer’s Monument.- 1 A Justification of Kummer’s Method.- 2 Basic Facts about the Arithmetic of Cyclotomic Fields.- 3 Kummer’s Main Theorem.- Lecture VI Regular Primes.- 1 The Class Number of Cyclotomic Fields.- 2 Bernoulli Numbers and Kummer’s 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 Kummer’s Congruences.- 5 Kummer’s 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 Fermat’s 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 ofFurtwängler.- 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.- Lecture X Fresh Efforts.- 1 Fermat’s Last Theorem Is True for Every Prime Exponent Less Than 125000.- 2 Euler Numbers and Fermat’s Theorem.- 3 The First Case Is True for Infinitely Many Pairwise Relatively Prime Exponents.- 4 Connections between Elliptic Curves and Fermat’s Theorem.- 5 Iwasawa’s Theory.- 6 The Fermat Function Field.- 7 Mordell’s Conjecture.- 8 The Logicians.- Lecture XI Estimates.- 1 Elementary (and Not So Elementary) Estimates.- 2 Estimates Based on the Criteria Involving Fermat Quotients.- 3 Thue, Roth, Siegel and Baker.- 4 Applications of the New Methods.- Lecture XII Fermat’s Congruence.- 1 Fermat’s Theorem over Prime Fields.- 2 The Local Fermat’s Theorem.- 3 The Problem Modulo a Prime-Power.- Lecture XIII Variations and Fugue on a Theme.- 1 Variation I (In the Tone of Polynomial Functions).- 2 Variation II (In the Tone of Entire Functions).- 3 Variation III (In the Theta Tone).- 4 Variation IV (In the Tone of Differential Equations).- 5 Variation V (Giocoso).- 6 Variation VI (In the Negative Tone).- 7 Variation VII (In the Ordinal Tone).- 8 Variation VIII (In a Nonassociative Tone).- 9 Variation IX (In the Matrix Tone).- 10 Fugue (In the Quadratic Tone).- Epilogue.- Index of Names.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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