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Prove that if p is a prime number p ≠ 3, then 3 divides p^2 + 2.

College level proof before real analysis. Please give formal proof.
Please explain each step of your solution. Thank you.

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It is proven that if p is a prime number p ≠ 3, then 3 divides p^2 + 2. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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