Number Theory and Geometry | PRMO 2019 | Problem 6

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.

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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