Contrapositives are confusing

[PsychonautQQ]

I'm a bit confused on how to apply contrapositives... This isn't for homework but I'm attempting to show that if n^2 + 2 is prime that 3|n.

I'm wondering if this is an appropriate time for me to show the contrapositive of the statement to be true, therefore the original statement to be true.

Contrapostive: if 3 does not divide n, then n^2+2 is not prime.

I know how to show this contrapositive to be true...

Am I doing this right?

 

[Svein]

I'm a bit confused on how to apply contrapositives... This isn't for homework but I'm attempting to show that if n^2 + 2 is prime that 3|n.

I'm wondering if this is an appropriate time for me to show the contrapositive of the statement to be true, therefore the original statement to be true.

Contrapostive: if 3 does not divide n, then n^2+2 is not prime.

I know how to show this contrapositive to be true...

Am I doing this right?

Yes.