March 19th, 2017, 11:32 AM  #1 
Newbie Joined: Mar 2017 From: sri lanka Posts: 3 Thanks: 0  if nx^2 then nx
1)if n is a positive integer and doesn't have a factor of any positive integer except 1 2)if x is an integer then, how to prove that if nx^2 then nx? 
March 19th, 2017, 01:17 PM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 6,446 Thanks: 2118 Math Focus: Mainly analysis and algebra 
1) You presumably mean "doesn't have a factor of any positive integer except $n$ and $1$". $n$ is prime, so you are going to refer to the prime factorisation of numbers, in particular that a prime factorisation is unique up to the order of the factors. 2) You might find it easier to prove the contrapositive: if $n$ does not divide $x$ then $n$ does not divide $x^2$. The two results are equivalent. 
March 19th, 2017, 01:29 PM  #3 
Newbie Joined: Mar 2017 From: sri lanka Posts: 3 Thanks: 0 
what if n can has factors of positive integers but not square factors?

March 19th, 2017, 04:12 PM  #4 
Math Team Joined: Dec 2013 From: Colombia Posts: 6,446 Thanks: 2118 Math Focus: Mainly analysis and algebra 
$n$ is prime by the definition you gave.
