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 March 19th, 2017, 11:32 AM #1 Newbie   Joined: Mar 2017 From: sri lanka Posts: 3 Thanks: 0 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 then, how to prove that if n|x^2 then n|x?
 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 contra-positive: if $n$ does not divide $x$ then $n$ does not divide $x^2$. The two results are equivalent. Thanks from Singi
 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.

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