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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**

**S**equence

Geometry

Number Theory

## Check the Answer

But try the problem first…

Answer: is 29.

Source

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

## Other useful links

- https://www.cheenta.com/cubes-and-rectangles-math-olympiad-hanoi-2018/
- https://www.youtube.com/watch?v=ST58GTF95t4&t=140s