|March 19th, 2017, 11:32 AM||#1|
Joined: Mar 2017
From: sri lanka
if n|x^2 then n|x
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
how to prove that if n|x^2 then n|x?
|March 19th, 2017, 01:17 PM||#2|
Joined: Dec 2013
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 contra-positive: if $n$ does not divide $x$ then $n$ does not divide $x^2$. The two results are equivalent.