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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5$\begingroup$ Have you tried a web search? Gerhard "Really, Have You Tried It?" Paseman, 2015.07.15 $\endgroup$– Gerhard PasemanJul 15, 2015 at 22:14
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$\begingroup$ Peek at imomath.com/index.php?options=615, for instance. $\endgroup$– vonbrandJul 23, 2015 at 1:16
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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... $\endgroup$– vonbrandJul 23, 2015 at 1:18
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$\begingroup$ 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. CookDec 6, 2015 at 3:33
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1 Answer
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(PDF download presentation from http://www.math.uconn.edu/~kconrad/.)
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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/.)
answered Nov 6, 2015 at 0:39