Number Theory

13 Lectures on Fermat's Last Theorem by Paulo Ribenboim PDF

By Paulo Ribenboim

Fermat's challenge, additionally ealled Fermat's final theorem, has attraeted the eye of mathematieians excess of 3 eenturies. Many shrewdpermanent equipment were devised to attaek the matter, and lots of appealing theories were ereated with the purpose of proving the theory. but, regardless of the entire makes an attempt, the query is still unanswered. The topie is gifted within the type of leetures, the place I survey the most strains of labor at the challenge. within the first leetures, there's a very short deseription of the early heritage, in addition to a seleetion of some of the extra consultant reeent effects. within the leetures whieh stick with, I study in sue eession the most theories eonneeted with the matter. The final lee tu res are approximately analogues to Fermat's theorem. a few of these leetures have been aetually given, in a shorter model, on the Institut Henri Poineare, in Paris, in addition to at Queen's collage, in 1977. I endeavoured to produee a textual content, readable by means of mathematieians commonly, and never in simple terms by way of speeialists in quantity thought. in spite of the fact that, as a result of a problem in dimension, i'm conscious that eertain issues will look sketehy. one other e-book on Fermat's theorem, now in coaching, will eontain a eonsiderable quantity of the teehnieal advancements passed over right here. it is going to serve those that desire to study those issues intensive and, i'm hoping, it's going to make clear and eomplement the current quantity.

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1929 vandiver, H. S. and Wahlin, G. Algebraic numbers, 11. Bull. Nat. Research Council, 62, 1928. Reprinted by Chelsea Publ. , New York, 1967. 1937 Bell, E. T. Men of Mathematics, Simon and Schuster, New York, 1937. 1943 Hofmann, J. E. Neues iiber Fermats zahlentheoretische Herausforderungen von 1657. Abhandl. Preuss. Akad. , Berlin, No. 9, 1944. 1948 Itard, J. Sur la date A attribuer A une lettre de Pierre Fermat. Revue &Histoire des Sciences et de leurs Applications 2, 1948,95-98. 1959 Schinzel, A.

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De I'Acad. des Sciences, Znstitut de France, 6, 1823, 1-60. 1825 Legendre, A. M. Essais sur la thiorie des nombres, 1825 (2nd supplement). Reprinted by SphinxOedipe, 4, 1909, 97-128. K. = Before Kummer 1828 Dirichlet, G. L. Memoire sur l'impossibilite de quelques equations indkterminees du 5' degre. J. reine u. , 3, 1828, 354-375. 1830 Legendre, A. M. ThPorie des Nombres, 3e edition, vol. 11, Firmin Didot Freres, Paris, 1830. Reprinted by A. Blanchard, Paris, 1955. ,1832 Dirichlet, G . L. Demonstration du theoreme de Fermat pour les 14' puissances.

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