Fermat's Last Theorem: A Genetic Introduction to Algebraic Number Theory (Google eBook)

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Springer Science & Business Media, 1977 - Mathematics - 410 pages
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This introduction to algebraic number theory via the famous problem of "Fermats Last Theorem" follows its historical development, beginning with the work of Fermat and ending with Kummers theory of "ideal" factorization. The more elementary topics, such as Eulers proof of the impossibilty of x+y=z, are treated in an uncomplicated 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 Kummers theory to quadratic integers and relates this to Gauss'theory of binary quadratic forms, an interesting and important connection that is not explored in any other book.
  

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Contents

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
Copyright

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Page vi - The sacred writers,' he observed, 'related the vicious as well as the virtuous actions of men ; which had this moral effect, that it kept mankind from despair, into which otherwise they would naturally fall, were they not supported by the recollection that others had offended like themselves...
Page 2 - On the other hand, it is impossible for a cube to be written as a sum of two cubes or a fourth power to be written as a sum of two fourth powers or, in general, for any number which is a power greater than the second to be written as a sum of two like powers. I have a truly marvelous demonstration of this proposition which this margin is too narrow to contain.
Page 403 - Arithmeticorum libri sex et de numeris multangulis liber unus. Cum commentariis CG BACHETI et observationibus DP DE FERMAT.

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About the author (1977)

Harold M. Edwards is Emeritus Professor of Mathematics at New York University. His previous books are Advanced Calculus (1969, 1980, 1993), Riemann's Zeta Function (1974, 2001), Fermat's Last Theorem (1977), Galois Theory (1984), Divisor Theory (1990) and Linear Algebra (1995). Readers of his Advanced Calculus will know that his preference for constructive mathematics is not new. In 1980 he was awarded the Steele Prize for mathematical exposition for the Riemann and Fermat books.

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