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# Number Theory | PRMO 2019 | Problem 3

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 $n\geq1$ 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

Sequence

Series

Number System

PRMO, 2019

Elementary Number Theory by David Burton

## Try with Hints

Here $$x_5=1+x_1x_2x_3x_4$$ then $$x_1x_2x_3x_4=42$$

$$x_6=1+x_1x_2x_3x_4x_5$$=1+(42)(43)=1807=(13)(139)

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

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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 $n\geq1$ 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

Sequence

Series

Number System

PRMO, 2019

Elementary Number Theory by David Burton

## Try with Hints

Here $$x_5=1+x_1x_2x_3x_4$$ then $$x_1x_2x_3x_4=42$$

$$x_6=1+x_1x_2x_3x_4x_5$$=1+(42)(43)=1807=(13)(139)

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

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