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.
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- $\begingroup$ Peek at imomath.com/index.php?options=615, for instance. $\endgroup$vonbrand– vonbrand2015-07-23 01:16:41 +00:00Commented Jul 23, 2015 at 1:16
- 5$\begingroup$ 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– vonbrand2015-07-23 01:18:38 +00:00Commented Jul 23, 2015 at 1:18
- 2$\begingroup$ 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. $\endgroup$James S. Cook– James S. Cook2015-12-06 03:33:23 +00:00Commented Dec 6, 2015 at 3:33
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1 Answer
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1 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 https://kconrad.math.uconn.edu/.)
- 2$\begingroup$ See also kconrad.math.uconn.edu/blurbs/ugradnumthy/pelleqn1.pdf and kconrad.math.uconn.edu/blurbs/ugradnumthy/pelleqn2.pdf $\endgroup$KCd– KCd2024-05-25 21:47:26 +00:00Commented May 25, 2024 at 21:47