How can Pell's equation be effectively introduced in elementary number theory?

[matqkks]

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.

 

[tommyxu3]

Here I have one of the interesting application of Pell's equation in the PDF below:
http://activity.ntsec.gov.tw/activity/race-2/2013/pdf/010031.pdf
and mind that its English version is below the Chinese one.