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

Divisibility Problem | PRMO 2019 | Question 8

Join Trial or Access Free Resources

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

Key Concepts


Inequalities

Algebra

Number Theory

Check the Answer


Answer: is 48.

PRMO, 2019, Question 8

Elementary Number Theory by David Burton

Try with Hints


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

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

Then n=48.

Subscribe to Cheenta at Youtube


Knowledge Partner

Cheenta is a knowledge partner of Aditya Birla Education Academy
Cheenta

Cheenta Academy

Aditya Birla Education Academy

Aditya Birla Education Academy

Cheenta. Passion for Mathematics

Advanced Mathematical Science. Taught by olympians, researchers and true masters of the subject.
JOIN TRIAL
support@cheenta.com
Menu
Trial
Whatsapp
Math Olympiad Program
magic-wandrockethighlight