Is 3 Divisible by n if 3 is Divisible by n^2?

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I'm completely lost on this one. I need this to be able to solve that the square root of three is irrational. So it's a proof within a proof, but I like this way best. Please help me out.
This is what I need to know how to prove.

3|n^2 implies 3|n where n is some integer.
 
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3 is a prime number. If 3 were not a prime factor of n, it could not be a factor of n2.
 
I think I understand what you're saying and that looks like a contrapositive proof, but you don't actually prove it. Could you elaborate?
 
cubicmonkey said:
I'm completely lost on this one. I need this to be able to solve that the square root of three is irrational. So it's a proof within a proof, but I like this way best. Please help me out.
This is what I need to know how to prove.

3|n^2 implies 3|n where n is some integer.

Suppose :

n \equiv a \pmod 3 ~\text{and}~ a \neq 0
then :
n^2 \equiv a^2 \pmod 3 ~\text{and}~ a^2 \neq 0
hence :
3 \nmid n^2
contradiction .

Q.E.D.
 
I think the Fundamental Theorem of Arithmetic (uniqueness up to order of prime factorizations) might help?
 
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