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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.

Source

Competency

Difficulty

Suggested Book

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.

First hint

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.

Second Hint

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.

- https://www.cheenta.com/divisibility-amc-8-2017-problem-7/
- https://www.youtube.com/watch?v=FNXm1dKvZ4I

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