The problem is based upon the divisibility and prime factorization of a numbers. Also we have to deal with the number divisible by either one prime number or more than one prime numbers.
A positive integer n is called a magic number if it has the following property: if a and b
are two positive numbers that are not coprime to n then a + b is also not coprime to n.
For example, 2 is a magic number, because sum of any two even numbers is also even.
Which of the following are magic numbers? Write your answers as a sequence of four
letters (Y for Yes and N for No) in correct order.
(i) 129 (ii) 128 (iii) 127 (iv) 100.
I.S.I. Entrance 2015 for B. sc. program at CMI Sub problem 3
Divisibility and Prime factorisation
6 out of 10
Secrets in Inequalities.
Take the LCM, and point out all the numbers that divides the given number, now select any two of them or any two of the prime factors out of calculated ones.
Now we can say those two prime factors a and b, and then we can easily calculate a+b. now check weather a+b and the number itself has any co prime factor or not other than 1.
I.S.I. & C.M.I. Entrance Program
Taught by students and alumni of I.S.I. & C.M.I.
In 2026, the following Cheenta students have been successful for Indian Statistical Institute's M.Stat Entrance. They ranked within the first 50 in the entire country in these entrances. I.S.I. M.Stat Entrance
In 2026, the following Cheenta students have been successful for Indian Statistical Institute's B.Stat Entrance and Chennai Mathematical Institute's B.Sc. Math Entrance. They ranked within the first 200 in the entire country in these entrances. Most of these students attended the problem solving workshops regularly, which happen 5 days every week. CMI B.Sc. Math Entrance […]
In 2025, 8 students from Cheenta Academy cracked the prestigious Regional Math Olympiad. In this post, we will share some of their success stories and learning strategies. The Regional Mathematics Olympiad (RMO) and the Indian National Mathematics Olympiad (INMO) are two most important mathematics contests in India.These two contests are for the students who are […]
Cheenta Academy proudly celebrates the success of 27 current and former students who qualified for the Indian Olympiad Qualifier in Mathematics (IOQM) 2025, advancing to the next stage — RMO. This accomplishment highlights their perseverance and Cheenta’s ongoing mission to nurture mathematical excellence and research-oriented learning.