How Cheenta works to ensure student success?
Explore the Back-Story

# Divisibility Problem | PRMO 2019 | Question 8

Try this beautiful problem from the PRMO, 2010 based on Divisibility.

## Divisibility Problem - PRMO 2019

Find the number of positive integers such that $3 \leq n \leq 98$ and $x^{2^{n}}+x+1$ is divisible by $x^{2}+x+1.$

• is 107
• is 48
• is 840
• cannot be determined from the given information

Inequalities

Algebra

Number Theory

## Check the Answer

PRMO, 2019, Question 8

Elementary Number Theory by David Burton

## Try with Hints

First hint

for n={3,5,...97}

Second Hint

where n is odd since factor of $x^{2}+x+1$ is also factor of given expression

Final Step

Then n=48.

## Subscribe to Cheenta at Youtube

Try this beautiful problem from the PRMO, 2010 based on Divisibility.

## Divisibility Problem - PRMO 2019

Find the number of positive integers such that $3 \leq n \leq 98$ and $x^{2^{n}}+x+1$ is divisible by $x^{2}+x+1.$

• is 107
• is 48
• is 840
• cannot be determined from the given information

Inequalities

Algebra

Number Theory

## Check the Answer

PRMO, 2019, Question 8

Elementary Number Theory by David Burton

## Try with Hints

First hint

for n={3,5,...97}

Second Hint

where n is odd since factor of $x^{2}+x+1$ is also factor of given expression

Final Step

Then n=48.

## Subscribe to Cheenta at Youtube

This site uses Akismet to reduce spam. Learn how your comment data is processed.

### Knowledge Partner

Cheenta is a knowledge partner of Aditya Birla Education Academy