MHB How Can Pell's Equation Enhance Elementary Number Theory?

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Pell's equation can be effectively introduced in elementary number theory through its historical context and connection to continued fractions. Practical applications include solving problems in Diophantine equations and cryptography. Interesting questions surrounding Pell's equation involve its solutions, properties, and connections to other mathematical concepts. Recommended resources for further exploration include textbooks and online lectures that focus on number theory. Understanding Pell's equation enriches the study of elementary number theory significantly.
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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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matqkks said:
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.

Hi everyone, :)

I just wanted to point out that this question was answered at,

https://www.linkedin.com/grp/post/4510047-6027195611164454913?trk=groups-post-b-title

so as to avoid duplication of effort.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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