MHB Questions on Pell's & Non-Linear Diophantine Equations UG Level

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Resources for Pell's and non-linear Diophantine equations at the undergraduate level include specific threads and forums dedicated to these topics. Pell's Equation is highlighted as particularly relevant, with suggestions to explore existing discussions on platforms like Math Help Boards. Users are encouraged to seek out interesting problems and results that can enhance their understanding. Engaging with these resources can provide valuable insights and practice opportunities. Overall, the forum serves as a useful starting point for students interested in these mathematical concepts.
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Are there any resources of questions on the topic of Pell's and non linear Diophantine equations? I am looking for interesting results which are required to be solved. This is for a typical second year undergraduate level.
Thanks.
 
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Have you looked at https://mathhelpboards.com/showthread.php?2905-The-Pell-Sequence in this forum?
 

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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