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  费马大定理
  ￥140.62元

这本专著介绍了著名的费马大定理的发展，从费马大定理起至Kummer的理论结束，以此介绍代数数论。而一些更基础的理论，如Euler证明x+y=z的不可能性，则以更简单的方式阐述。一些新的理论和工具则通过具体问题加以介绍。这本专著还详细介绍了Kummer理论在二次积分的应用及其与Gauss理论的联系，这部分理论在其他专著中都未曾有过介绍。

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• Chapter 1 Fermat
  1.1 Fermat and his'Last Theorem'
  1.2 Pythagorean triangles
  1.3 How to find Pythagorean triples
  1.4 The method of infinite descent
  1.5 The case n=4 of the Last Theorem
  1.6 Fermat's one proof
  1.7 Suns of two squares and related topics
  1.8 Perfect numbers and Fermat's theorem
  1.9 Pell's equation
  1.10 Other number-theoretic discoveries of Fermat
  Chapter 2 Euler
  2.1 Euler and the case n=3
  2.2 Euler's proof of the case n=3
  2.3 Arithmetic of surds
  2.4 Euler on sums of two squares
  2.5 Remainder of the proof when n=3
  2.6 Addendum on sums of two squares
  Chapter 3 From Euler to Kummer
  3.1 Introduction
  3.2 Sophie Germain's theorem
  3.3 The case n=5
  3.4 The cases n=14 and n=7
  Chapter 4 Kummer's theory of ideal factors
  4.1 The events of 1847
  4.2 Cyclotomic integers
  4.3 Factorization of primes p*1 mod λ
  4.4 Computations when p*1 mod λ
  4.5 Periods
  4.6 Factorization of primes p≠1 mod λ
  4.7 Computations when p≠1 mod λ
  4.8 Extension of divisibility test
  4.9 Prime divisors
  4.10 Multiplicities and the exceptional prime
  4.11 The fundamental theorem
  4.12 Divisors
  4.13 Terminology
  4.14 Conjugations and the norm of a divisor
  4.15 Summary
  Chapter 5 fermat's Last Theorem for regular primes
  5.1 Kummer's remarks on quadratic integers
  5.2 Equivalence of divisors in a special case
  5.3 The class number
  5.4 Kummer's two conditions
  5.5 The proof for regular primes
  5.6 Quadratic reciprocity
  Chapter 6 Determination of the class number
  6.1 Introduction
  6.2 The Euler product formula
  6.3 First steps
  6.4 Reformulation of the right side
  6.5 Dirichlet's evaluation of L(l,x)
  6.6 The limit of the right side
  6.7 The nonvanishing of L-series
  6.8 Reformulation of the left side
  6.9 Units:The first few cases
  6.10 Units:the general case
  6.11 Evaluation of the integral
  6.12 Comparison of the integral and the sum
  6.13 The sum over other divisor classes
  6.14 The class number formula
  6.15 proof that 37 is irregular
  6.16 Divisibility of the first factor by λ
  6.17 Divisibility of the second factor by λ
  6.18 Kummer's lamma
  6.19 Summary
  Chapter 7 Divisor theory for quadratic integers
  7.1 The prime divisors
  7.2 The divisor theory
  7.3 The sign of the norm
  7.4 Quadratic integers with given divisors
  7.5 Validity of the cyclic method
  7.6 The divisor class group:examples
  7.7 The divisor class group:a general theorem
  7.8 Euler's theorems
  7.9 Genera
  7.10 Ambiguous divisors
  7.11 Gauss's second proof of quadratic reciprocity
  Chapter 8 Gauss's theory of binary quadratic forms
  8.1 Other divisor class groups
  8.2 Alternative view of the cyclic method
  8.3 The correspondence between divsors and binary quadratic forms
  8.4 The classification of forms
  8.5 Examples
  8.6 Gauss's composition of forms
  8.7 Equations of degree 2 in 2 variables
  Chpater 9 Dirichlet's class number formula
  9.1 The euler product formula
  9.2 First case
  9.3 Another case
  9.4 D≡1 mod 4
  9.5 Evaluation of Σ(^D_n)1/n
  9.6 Suborders
  9.7 Primes in arithmetic progressions
  Appendix:The natural numbers
  A.1 Basic properties
  A.2 primitive roots mod p
  Answers to exercises
  Bibliography
  Index