Cookies must be enabled to use this web application.

To allow this site to use cookies, use the steps that apply to your browser below. If your browser is not listed below, or if you have any questions regarding this site, please contact us.

Microsoft Internet Explorer
  • 1. Select "Internet Options" from the Tools menu.
  • 2. Click on the "Privacy" tab.
  • 3. Click the "Default" button.
  • 4. Click "OK" to save changes.
Chrome Chrome
  • 1. Click the "Spanner" icon in the top right of the browser.
  • 2. Click Options and change to the "Under the Hood" tab.
  • 3. Scroll down until you see "Cookie settings:".
  • 4. Set this to "Allow all cookies".
Firefox Firefox
  • 1. Go to the "Tools" menu and select "Options".
  • 2. Click the "Privacy" icon on the top of the window.
  • 3. Click on the "Cookies" tab.
  • 4. Check the box corresponding to "Allow sites to set Cookies.
  • 5. Click "OK" to save changes.
Opera Opera
  • 1. Click on the "Tools" menu and then click Preferences.
  • 2. Change to the Advanced tab, and to the cookie section.
  • 3. Select "Accept cookies only from the site I visit" or "Accept cookies".
  • 4. Ensure "Delete new cookies when exiting Opera" is not ticked.
  • 5. Click OK.
Netscape and Mozilla Suite Netscape and Mozilla Suite
  • 1. Select "Preferences" from the Edit menu.
  • 2. Click on the arrow next to "Privacy & Security".
  • 3. Under "Privacy & Security" select "Cookies".
  • 4. Select "Enable all cookies".
  • 5. Click "OK" to save changes.
Safari Safari
  • 1. Click on the "Cog" icon in Safari.
  • 2. Click Preferences.
  • 3. Change to the Security tab.
  • 4. Select "Only from sites I visit" or "Allow".
  • 5. Close the dialog using the cross.
Book Image Not Available Book Image Not Available
Book details
  • Genre:MATHEMATICS
  • SubGenre:Number Theory
  • Language:English
  • Pages:310
  • Format:Paperback
  • Paperback ISBN:9781098327965

Understanding Anatomy of Exponential Diophantine 3-term Equations

by Rajen Merchant

Book Image Not Available Book Image Not Available
Overview
This book develops a classification structure to classify solutions to exponential diophantine 3-term equations. This classification is utilized in understanding of various equations starting from A + B = C to the Fermat's equation and the Beal equation. It is shown that for Fermat's equation, non-primitive solutions cannot exist unless primitive solutions exist. For Beal's equation, non-primitive solutions can exist even if primitive solutions may not exist.
Description
This monograph is specially written for students and researchers in mathematics, particularly number theory. Professors and instructors teaching this subject will find it very useful. This monograph develops a clear understanding of the structure of the exponential diophantine 3-term equations and their solutions. Various components of an exponential diophantine equation and their roles are described in detail. A combinatorial approach is used to classify and analyze solutions to exponential diophantine 3-term equations. To classify these solutions, all possible ways these solutions can occur are examined. The analysis presented reveals that these solutions can be classified into three classes and six sub-classes. Properties of each class of solutions are described in detail. We observe that each exponential diophantine 3-term equation imposes its own requirements on its solutions. We discuss how these requirements of an exponential diophantine equation can affect solutions in each class. We apply the classification developed here to relate to the results for the Pythagorean equation, the Catalan equation, and the Ramanujan-Nagell equation. Finally, we employ the concepts developed in this monograph and present twelve proofs and four conjectures that help us analyze and understand the Fermat's Last Theorem and the Beal's conjecture. These four conjectures are much smaller in scope.
About the author
Rajen Merchant studied at Bombay University for one year and then graduated as Bachelor of Technology (a five year course) at the Indian Institute of Technology, Bombay, India. After completing his Master of Science at Carnegie-Mellon University, Pittsburgh, USA, he migrated to Canada. He obtained his Master of Business Administration degree from Queen's University, Kingston, Canada. He has a keen interest in mathematics and its applications. His pursuit for mathematical accuracy has helped him better understand the intricacies of the exponential Diophantine equations as well as the elliptical co-ordinate system. This is his third monograph. The first monograph, titled "Understanding the Elastic Stress Field Around an Elliptical Hole in a Thin Plate (in the deformed configuration)" – ISBN 978-1-48359-262-6, was published in January 2017. The second monograph, titled "Understanding Non-Linear Strain-Displacement Relations in the Elliptical Co-ordinate System (with applications to holes in a thin plate)" - ISBN 978-1-54398-916-8, was published in December 2019. He intends to publish the fourth book soon. This fourth book will examine applications of the concepts presented in the first two monographs.
Thanks for submitting a review!

Your review will need to be approved by the author before being posted.

See Inside
Front Cover

Loading book cover...

Book Image Not Available Book Image Not Available
Session Expiration WarningYour session is due to expire.

Your online session is due to expire shortly.
Would you like to extend your session and remain logged in?

Session Expired

Your session has expired.We're sorry, but your online session has expired.
Please log back into your account to continue.

This site uses cookies. Continuing to use this site without changing your cookie settings means that you consent to those cookies to enhance site navigation and the overall user experience. Learn more about our privacy policy or learn more about how to turn off cookies.