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＜電子ブック＞
Fermat’s Last Theorem for Amateurs / by Paulo Ribenboim

版	1st ed. 1999.
出版者	New York, NY : Springer New York : Imprint: Springer
出版年	1999
本文言語	英語
大きさ	XIII, 407 p : online resource
冊子体	Fermat's last theorem for amateurs / Paulo Ribenboim
著者標目	*Ribenboim, Paulo author SpringerLink (Online service)
件　名	LCSH:Number theory FREE:Number Theory
一般注記	The Problem -- Special Cases -- 4 Interludes -- Algebraic Restrictions on Hypothetical Solutions -- Germain’s Theorem -- Interludes 5 and 6 -- Arithmetic Restrictions on Hypothetical Solutions and on the Exponent -- Interludes 7 and 8 -- Reformulations, Consequences, and Criteria -- Interludes 9 and 10 -- The Local and Modular Fermat Problem -- Epilogue ItisnowwellknownthatFermat’slasttheoremhasbeenproved. For more than three and a half centuries, mathematicians — from the greatnamestothecleveramateurs—triedtoproveFermat’sfamous statement. The approach was new and involved very sophisticated theories. Finallythelong-soughtproofwasachieved. Thearithmetic theory of elliptic curves, modular forms, Galois representations, and their deformations, developed by many mathematicians, were the tools required to complete the di?cult proof. Linked with this great mathematical feat are the names of TANI- YAMA, SHIMURA, FREY, SERRE, RIBET, WILES, TAYLOR. Their contributions, as well as hints of the proof, are discussed in the Epilogue. This book has not been written with the purpose of presentingtheproofofFermat’stheorem. Onthecontrary, itiswr- ten for amateurs, teachers, and mathematicians curious about the unfolding of the subject. I employ exclusively elementary methods (except in the Epilogue). They have only led to partial solutions but their interest goes beyond Fermat’s problem. One cannot stop admiring the results obtained with these limited techniques. Nevertheless, I warn that as far as I can see — which in fact is not much — the methods presented here will not lead to a proof of Fermat’s last theorem for all exponents. vi Preface The presentation is self-contained and details are not spared, so the reading should be smooth. Most of the considerations involve ordinary rational numbers and only occasionally some algebraic (non-rational) numbers. For this reason I excluded Kummer’s important contributions, which are treated in detail in my book, Classical Theory of Algebraic N- bers and described in my 13 Lectures on Fermat’s Last Theorem (new printing, containing an Epilogue about recent results) Accessibility summary: This PDF is not accessible. It is based on scanned pages and does not support features such as screen reader compatibility or described non-text content (images, graphs etc). However, it likely supports searchable and selectable text based on OCR (Optical Character Recognition). Users with accessibility needs may not be able to use this content effectively. Please contact us at accessibilitysupport@springernature.com if you require assistance or an alternative format Inaccessible, or known limited accessibility No reading system accessibility options actively disabled Publisher contact for further accessibility information: accessibilitysupport@springernature.com HTTP:URL=https://doi.org/10.1007/b97437

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