Catalan's Conjecture

Nonfiction, Science & Nature, Mathematics, Number Theory, Algebra
Cover of the book Catalan's Conjecture by René Schoof, Springer London
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: René Schoof ISBN: 9781848001855
Publisher: Springer London Publication: July 8, 2010
Imprint: Springer Language: English
Author: René Schoof
ISBN: 9781848001855
Publisher: Springer London
Publication: July 8, 2010
Imprint: Springer
Language: English

Eugène Charles Catalan made his famous conjecture – that 8 and 9 are the only two consecutive perfect powers of natural numbers – in 1844 in a letter to the editor of Crelle’s mathematical journal. One hundred and fifty-eight years later, Preda Mihailescu proved it.

Catalan’s Conjecture presents this spectacular result in a way that is accessible to the advanced undergraduate. The author dissects both Mihailescu’s proof and the earlier work it made use of, taking great care to select streamlined and transparent versions of the arguments and to keep the text self-contained. Only in the proof of Thaine’s theorem is a little class field theory used; it is hoped that this application will motivate the interested reader to study the theory further.

Beautifully clear and concise, this book will appeal not only to specialists in number theory but to anyone interested in seeing the application of the ideas of algebraic number theory to a famous mathematical problem.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

Eugène Charles Catalan made his famous conjecture – that 8 and 9 are the only two consecutive perfect powers of natural numbers – in 1844 in a letter to the editor of Crelle’s mathematical journal. One hundred and fifty-eight years later, Preda Mihailescu proved it.

Catalan’s Conjecture presents this spectacular result in a way that is accessible to the advanced undergraduate. The author dissects both Mihailescu’s proof and the earlier work it made use of, taking great care to select streamlined and transparent versions of the arguments and to keep the text self-contained. Only in the proof of Thaine’s theorem is a little class field theory used; it is hoped that this application will motivate the interested reader to study the theory further.

Beautifully clear and concise, this book will appeal not only to specialists in number theory but to anyone interested in seeing the application of the ideas of algebraic number theory to a famous mathematical problem.

More books from Springer London

Cover of the book Data Mining in Large Sets of Complex Data by René Schoof
Cover of the book Reproductive Surgery in Assisted Conception by René Schoof
Cover of the book Kenaf: A Multi-Purpose Crop for Several Industrial Applications by René Schoof
Cover of the book Endocrinology and Diabetes by René Schoof
Cover of the book Proofs and Algorithms by René Schoof
Cover of the book Terminology and Terminological Systems by René Schoof
Cover of the book Placental Function Tests by René Schoof
Cover of the book Probability Theory by René Schoof
Cover of the book High-Risk IV Medications in Special Patient Populations by René Schoof
Cover of the book Polyhedral and Algebraic Methods in Computational Geometry by René Schoof
Cover of the book Pelvic Cancer Surgery by René Schoof
Cover of the book S-Variable Approach to LMI-Based Robust Control by René Schoof
Cover of the book Interactive Media: The Semiotics of Embodied Interaction by René Schoof
Cover of the book Sexually Transmitted Diseases by René Schoof
Cover of the book Difficult Cases in Endourology by René Schoof
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy