# Resources for Pell's equation

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.

• Have you tried a web search? Gerhard "Really, Have You Tried It?" Paseman, 2015.07.15 – Gerhard Paseman Jul 15 '15 at 22:14
• Peek at imomath.com/index.php?options=615, for instance. – vonbrand Jul 23 '15 at 1:16
• If you don't know how it fits into your course, and why you'd want to consider it, better leave it out... – vonbrand Jul 23 '15 at 1:18
• 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. – James S. Cook Dec 6 '15 at 3:33

## 1 Answer

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/.)