What is the best way to introduce Pell’s equation on a first elementary number theory course? Are there any practical applications of Pell’s equation? What are the really interesting questions about Pell’s equation? Are there any good resources on Pell’s equation.

  • 5
    $\begingroup$ Have you tried a web search? Gerhard "Really, Have You Tried It?" Paseman, 2015.07.15 $\endgroup$ Jul 15 '15 at 22:14
  • $\begingroup$ Peek at imomath.com/index.php?options=615, for instance. $\endgroup$
    – vonbrand
    Jul 23 '15 at 1:16
  • 4
    $\begingroup$ If you don't know how it fits into your course, and why you'd want to consider it, better leave it out... $\endgroup$
    – vonbrand
    Jul 23 '15 at 1:18
  • $\begingroup$ There is a nice chapter in Stillwell's number theory text. It has a bit about the rational approximation mentioned in the answer below. Also, the problem of finding the first solution from which the others can be generated is considered in that chapter. $\endgroup$ Dec 6 '15 at 3:33

Keith Conrad gave a presentation in 2008 that addresses your question, e.g.:

Pell solutions lead to good rational approximations to $\sqrt{d}$:

          (PDF download presentation from http://www.math.uconn.edu/~kconrad/.)


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.