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Infinite Sums, Diophantine Equations and Fermat’s Last Theorem

  • Henri Darmon
  • Claude Levesque
Part of the Developments in Mathematics book series (DEVM, volume 8)

Abstract

Thanks to the results of Andrew Wiles, we know that Fermat’s last theorem is true. As a matter of fact, this result is a corollary of a major result of Wiles: every semi-stable elliptic curve over Q is modular. The modularity of elliptic curves over Q is the content of the Shimura-Taniyama conjecture, and in this lecture, we will restrain ourselves to explaining in elementary terms the meaning of this deep conjecture.

Keywords

diophantine equation elliptic curve Fermat’s last theorem Fermat—Pell equation modular form Pythagoras’ equation 

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Copyright information

© Springer Science+Business Media Dordrecht 2002

Authors and Affiliations

  • Henri Darmon
    • 1
  • Claude Levesque
    • 2
  1. 1.CICMA, Mathematics Dept.McGILL UniversityMontréalCanada
  2. 2.CICMA, Dép. de Mathématiques et de StatistiqueUniversité LavalQuébecCanada

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