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 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
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