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Number Theory and Geometry | PRMO 2019 | Problem 6

Try this beautiful problem from Pre RMO 2019 based on Number Theory and Geometry. You may use sequential hints to solve the problem.

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


Sequence

Geometry

Number Theory

Check the Answer


Answer: is 29.

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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