Try this beautiful problem from Pre RMO 2019 based on Number Theory and Geometry.

Number Theory and Geometry – PRMO 2019

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.

  • is 13
  • is 29
  • is 840
  • cannot be determined from the given information

Key Concepts



Number Theory

Check the Answer

But try the problem first…

Answer: is 29.

Suggested Reading

PRMO, 2019

Elementary Number Theory by David Burton

Try with Hints

First hint

Here a,b,c form Pythagoras triplet then abc=345 or 435

Second Hint

345=(3)(5)(23) and 435=(5)(3)(29)

Final Step

Then largest possible prime factor=29

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