A fourteenth lecture on Fermat’s Last Theorem∗
نویسنده
چکیده
The title of this lecture alludes to Ribenboim’s delightful treatise on Fermat’s Last Theorem [Rib1]. Fifteen years after the publication of [Rib1], Andrew Wiles finally succeeded in solving Fermat’s 350-year-old conundrum. That same year, perhaps to console himself of Fermat’s demise, Ribenboim published a second book, this time on Catalan’s conjecture that there are no consecutive perfect powers other than 8 and 9. As we have learned at this Congress, Preda Mihailescu has just disposed of this conjecture as well. His breakthrough comes only 8 years after the publication of Ribenboim’s book on Catalan’s equation. Such is the magic of Ribenboim’s books: the age-old problems which they treat have invariably been solved, in comparatively short order! So it is with some eagerness that we await the publication of Ribenboim’s next tome (hoping it will be devoted to the Riemann Hypothesis, or the Birch and Swinnerton-Dyer conjecture...) This “fourteenth lecture” is meant as a tribute both to Ribenboim and to the spirit of Fermat: the fascination with concrete Diophantine problems, especially those that draw us, seemingly inexorably, to central topics in the subject (cyclotomic fields, elliptic curves, reciprocity laws, modular forms...)
منابع مشابه
Modular Forms and Diophantine Questions
This article discusses many of the topics that I touched on during my Public Lecture at the National University of Singapore and my Lecture to Schools at Victoria Junior College. During the former lecture, I spoke in broad terms about the history of Fermat’s Last Theorem and about the connection between Fermat’s Last Theorem, and the conjecture—now a theorem!—to the effect that elliptic curves ...
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