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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.

## 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

Sequence

Geometry

Number Theory

## Check the Answer

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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