First off, since that would mean p is divisible by something other than 1 and itself and we already said
So just go through the other two cases:
If then
If then ........... Finish it off.
Prove that if p is a prime number and p does not equal 3, then 3 divides . I'm given a hint that says, "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 understand the hint and the initial statement, I just don't know where to start.
Gotcha. Thanks for the help. I have one more question that is somewhat on topic.
We are proving things in class but only in the sense that we have to take the work someone else has done and assume it's true. At some point in a proof do you just have to use common sense. For example, "Let k be an integer. Then is even and is odd." What does the proof for either of those look like?