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Number Theoretic Methods pp 73–95Cite as

Infinite Sums, Diophantine Equations and Fermat’s Last Theorem

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Part of the book series: Developments in Mathematics ((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.

Written English version of a lecture given in French by Henri Darmon on October 14, 1995, at CEGEP de Lévis-Lauzon on the occasion of the Colloque des Sciences Mathématiques du Québec and which appeared in French in the Comptes Rendus du 38e Congrès de l’Association Mathématique du Québec

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Author information

Authors and Affiliations

  1. CICMA, Mathematics Dept., McGILL University, Montréal, Canada, H3A 2K6

    Henri Darmon

  2. CICMA, Dép. de Mathématiques et de Statistique, Université Laval, Québec, Canada, G1K 7P4

    Claude Levesque

Authors
  1. Henri Darmon
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  2. Claude Levesque
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Editor information

Editors and Affiliations

  1. Graduate School of Advanced Technology, University of Kinki, Iizuka, Japan

    Shigeru Kanemitsu

  2. Institute of Mathematics, Academia Sinica, Beijing, China

    Chaohua Jia

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Darmon, H., Levesque, C. (2002). Infinite Sums, Diophantine Equations and Fermat’s Last Theorem. In: Kanemitsu, S., Jia, C. (eds) Number Theoretic Methods. Developments in Mathematics, vol 8. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3675-5_6

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  • DOI: https://doi.org/10.1007/978-1-4757-3675-5_6

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