- #1

opt!kal

- 19

- 0

I've been having a lot of trouble with this particular proof lately, and I just do not know how to finish it up:

## Homework Statement

Show that if n is a perfect square, then n+2 is not a perfect square.(show by contradiction)

## Homework Equations

none that I know of

## The Attempt at a Solution

Since its a proof by contradiction, I know that I can rewrite it in the form: p ^ not q.

So I have: n is a perfect square, and n+2 is a perfect square.

Since I assume that then I have that n = k^2 and n+2 = p^2

So then I'll have (k^2) + 2 = p^2

At this point I basically get confused. I just have no idea on how to proceed from here, my only guess is that I should do two cases, one where k is even and one where k is odd, and show for each case that p^2 will end up like the case, while p will end up as the opposite (i.e. if I do the even case, then try to show that p will end up odd). But I have absolutely no idea on how to accomplish that. Any help would be greatly appreciated!