Try this beautiful problem from Pre RMO 2019 based on Number Theory and Geometry.
Let abc be a three digit number with nonzero digits such that \(a^{2}+b^{2}=c^{2}\). Find is the largest possible prime factor of abc.
Sequence
Geometry
Number Theory
Answer: is 29.
PRMO, 2019
Elementary Number Theory by David Burton
Here a,b,c form Pythagoras triplet then abc=345 or 435
345=(3)(5)(23) and 435=(5)(3)(29)
Then largest possible prime factor=29
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