cmi-entrance 2015 Q3

cmi-entrance · India · ugmath 4 marks Number Theory Prime Number Properties and Identification
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.
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.