I designed this simple math puzzle last week:
Prove or disprove the following statement:
- Claim: Let
be positive integers such that
and
. Given two rational numbers
, there exist positive integers
such that
and
and
is a perfect square.
- If the above statement is true, show an example of
- If the above statement is false, construct a counterexample.
Leave your solutions in the comments. Have fun solving it.
My Brain is Open 
My solution was a bit too long for a comment, but you can read it at https://grossack.site/2021/11/16/dense-pythagorean-triples.html ^_^
Hi Chris, Your diagrams and the detailed explanations of proofs are awesome 🙂 I have posted a follow up puzzle at https://kintali.wordpress.com/2021/11/16/density-of-pythagorean-triplets-part-2/ Have fun solving it 🙂
Pingback: Density of pythagorean triplets – Part 2 – My Brain is Open