Description

Book Synopsis
Challenge: Can you find all the integers $a$, $b$, $c$ satisfying $2a^{2} + 3b^{2} = 5c^{2}$? Looks simple, and there are in fact a number of easy solutions. But most of them turn out to be anything but obvious! A major advance in number theory means this book can give an easy answer to this and countless similar questions.

Table of Contents
  • A marriage for the ages
  • Viewing the whole algebraic curve
  • Entering the world of elliptic curves
  • Every elliptic curve is a group!
  • A million-dollar challenge
  • Every real elliptic curve lives in a donut
  • The genus
  • In conclusion $\ldots$
  • What is a smooth complex curve?
  • Algebraic curves in the disk model
  • Some code for this books's programs
  • Bibliography
  • Index

A Gateway to Number Theory Applying the Power of

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    A Paperback by Keith Kendig

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      Publisher: MP-AMM American Mathematical
      Publication Date: 6/30/2021 12:00:00 AM
      ISBN13: 9781470456221, 978-1470456221
      ISBN10: 1470456222

      Description

      Book Synopsis
      Challenge: Can you find all the integers $a$, $b$, $c$ satisfying $2a^{2} + 3b^{2} = 5c^{2}$? Looks simple, and there are in fact a number of easy solutions. But most of them turn out to be anything but obvious! A major advance in number theory means this book can give an easy answer to this and countless similar questions.

      Table of Contents
      • A marriage for the ages
      • Viewing the whole algebraic curve
      • Entering the world of elliptic curves
      • Every elliptic curve is a group!
      • A million-dollar challenge
      • Every real elliptic curve lives in a donut
      • The genus
      • In conclusion $\ldots$
      • What is a smooth complex curve?
      • Algebraic curves in the disk model
      • Some code for this books's programs
      • Bibliography
      • Index

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