Prove 1-n^2>0: 3n-2 is Even Integer

[bonfire09]

Let nεZ,Prove that 1-n^2>0, then 3n-2 is an even integer.

I proved it like this. I think its right but I am not able to word it correctly.

Since 1-n^2>0 therefore n=0. Then 3n-6=3(0)-2=-2. Since 0 is an integer, 3n-6 is even.

How can I learn to word this correctly because I am having some trouble with it?

 

[haruspex]

Are you sure you have the statement of the problem correct? It looks crazy. As you say 1 - n² > 0 would imply n = 0, which makes the rest of it much too easy. Also, why would anyone ask you to prove 3n-2 is an even integer when n is already known to be an integer? Why not just ask you to show n is even?