Prove that if p is a prime number and p is not equal to 3 then 3 divides p^2+2. (HINT:When p is divided by 3, the remainder is either 0, 1, or 2....i.e. for some k, p=3k or 3k+1 or 3k+2....)
Ok, so for p to be prime, it has only 2 positive divisors (1 and itself).
I tried doing this with a contradiction and assuuming 3 does not divide p^2+2, but I got a bit confused.
I also tried something along the lines of Assume p is prime, then p=pk or p=1k for some integer k. But that just confused me. What can I do?