rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    non sort: The
    title: Problem of Catalan
  name:
    name part: Bilu, Yuri F.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Bugeaud, Yann.
    role:
      role term: author.
  name:
    name part: Mignotte, Maurice.
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2014
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XIV, 245 p. 3 illus. online resource.
  abstract: In 1842 the Belgian mathematician Eugène Charles Catalan asked whether 8 and 9 are the only consecutive pure powers of non-zero integers. 160 years after, the question was answered affirmatively by the Swiss mathematician of Romanian origin Preda Mihăilescu. In this book we give a complete and (almost) self-contained exposition of Mihăilescu’s work, which must be understandable by a curious university student, not necessarily specializing in Number Theory. We assume very modest background: a standard university course of algebra, including basic Galois theory, and working knowledge of basic algebraic number theory.
  table of contents: An Historical Account -- Even Exponents -- Cassels' Relations -- Cyclotomic Fields -- Dirichlet L-Series and Class Number Formulas -- Higher Divisibility Theorems -- Gauss Sums and Stickelberger's Theorem -- Mihăilescu’s Ideal -- The Real Part of Mihăilescu’s Ideal -- Cyclotomic units -- Selmer Group and Proof of Catalan's Conjecture -- The Theorem of Thaine -- Baker's Method and Tijdeman's Argument -- Appendix A: Number Fields -- Appendix B: Heights -- Appendix C: Commutative Rings, Modules, Semi-Simplicity -- Appendix D: Group Rings and Characters -- Appendix E: Reduction and Torsion of Finite G-Modules -- Appendix F: Radical Extensions.
  note: by Yuri F. Bilu, Yann Bugeaud, Maurice Mignotte.
  subject:
    topic: Mathematics
  subject:
    topic: Algebra
  subject:
    topic: Number theory
  subject:
    topic: Mathematics
  subject:
    topic: Number Theory
  subject:
    topic: General Algebraic Systems
  subject:
    topic: Algebra
  classification: QA241-247.5
  classification: 512.7
  related item:
    title info:
      title: Springer eBooks
  identifier: 9783319100944
  identifier: http://dx.doi.org/10.1007/978-3-319-10094-4
  record info:
    record creation date: 141009
    record change date: 20141009193309.0
    record identifier: 978-3-319-10094-4