Try this beautiful problem from Pre RMO, 2019 based on the Number theory.

Number Theory – PRMO 2019

Let \(x_1\) be a positive real number and for every integer n>=1 let \(x_{n+1}=1+x_{1}x_{2}…x_{n-1}x_{n}\). If \(x_{5}=43\). what is the sum of digits of the largest prime factor of \(x_{6}\).

  • is 13
  • is 25
  • is 840
  • cannot be determined from the given information

Key Concepts



Number System

Check the Answer

But try the problem first…

Answer: is 13.

Suggested Reading

PRMO, 2019

Elementary Number Theory by David Burton

Try with Hints

First hint

Here \(x_5=1+x_1x_2x_3x_4\) then \(x_1x_2x_3x_4=42\)

Second Hint


Final Step

Then largest prime factor=139 then sum of digits=13

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