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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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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