Fermat's Last Theorem: A Genetic Introduction to Algebraic Number Theory

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Springer Science & Business Media, 14 janv. 2000 - 407 pages
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This book is an introduction to algebraic number theory via the famous problem of "Fermat's Last Theorem." The exposition follows the historical development of the problem, beginning with the work of Fermat and ending with Kummer's theory of "ideal" factorization, by means of which the theorem is proved for all prime exponents less than 37. The more elementary topics, such as Euler's proof of the impossibilty of x+y=z, are treated in an elementary way, and new concepts and techniques are introduced only after having been motivated by specific problems. The book also covers in detail the application of Kummer's ideal theory to quadratic integers and relates this theory to Gauss' theory of binary quadratic forms, an interesting and important connection that is not explored in any other book.
 

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Table des matières

Fermat
1
Euler
39
From Euler to Kummer
59
Kummers theory of ideal factors
76
Fermats Last Theorem for regular primes
152
Determination of the class number
181
Divisor theory for quadratic integers
245
Gausss theory of binary quadratic forms
305
Dirichlets class number formula
342
The natural numbers
372
Answers to exercises
381
Bibliography
403
Index
409
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Page 403 - Arithmeticorum libri sex et de numeris multangulis liber unus. Cum commentariis CG BACHETI et observationibus DP DE FERMAT.

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