基本説明
Presents partial results which could be obtained with exclusively elementary methods. The proofs are given in detail with minimal prerequisites.
Full Description
In 1995, Andrew Wiles completed a proof of Fermat's Last Theorem. Although this was certainly a great mathematical feat, one shouldn't dismiss earlier attempts made by mathematicians and clever amateurs to solve the problem. In this book, aimed at amateurs curious about the history of the subject, the author restricts his attention exclusively to elementary methods that have produced rich results.
Contents
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.