I Exploring Interesting Mathematical Puzzles

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The discussion focuses on sharing and solving intriguing mathematical puzzles. Participants are encouraged to post their own puzzles or challenge others with favorites. An initial puzzle involves a farmer wanting to split a rectangular field into two equal parts, with a suggested solution of drawing a diagonal to demonstrate congruence. Another puzzle presented seeks the least odd positive integer m that satisfies a specific equation involving n. The conversation emphasizes the enjoyment of collaborative problem-solving in mathematics.
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Let's discuss and solve some intriguing mathematical puzzles. Share your favorite puzzles and solutions!
I thought it would be fun to start a thread where we can share and discuss interesting mathematical puzzles. Whether you have a puzzle you've been pondering or a favorite one you'd like to challenge others with, feel free to post it here. Let's see how many we can solve together!

Here's one to get us started:Puzzle:
A farmer has a rectangular field and wants to split it into two equal parts. What is the simplest way to do this, and how can we prove that both parts are indeed equal?
 
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Draw the diagonal, done. Equality follows from congruence. It can also be done with a compass and a straightedge.

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How about that one?

What is the least odd, positive integer ##m## such that
$$
n^2=(m+164)(m^2+164^2)
$$
for some integer ##n##?

Elegant solution: 1 page.
Brute force: 2 pages.

But maybe there is even a shorter clue than the one I have found.
 
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