posted by Meg .
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. That is, for some integer k, p = 3k or p = 3k + 1 or p = 3k + 2.)
I thought you might do three cases with the three values of p in the hint, plugging them into p^2+2. In two of the cases you get a p^2+2=3a (a some integer) form but for p=3k you do not. Am I approaching this wrong?