Contrapositives are confusing

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To prove that if n^2 + 2 is prime, then 3 divides n, the contrapositive approach is valid. The contrapositive statement is that if 3 does not divide n, then n^2 + 2 is not prime. This method is a standard logical technique in mathematics, confirming the original statement's validity through its contrapositive. The user expresses confidence in their ability to demonstrate the contrapositive's truth. Overall, the discussion clarifies the correct application of contrapositives in mathematical proofs.
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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?
 
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PsychonautQQ said:
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.
 
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