The discussion revolves around a GCSE past paper question that asks to prove algebraically that the sum of the squares of any two consecutive even integers is never a multiple of 8. Participants are examining the representation of consecutive even integers and the validity of the proof approach suggested by the original poster.
The discussion is ongoing, with participants providing feedback on the original poster's approach and questioning the necessity of proof by contradiction. There is a lack of consensus on the method to be used, and some participants are seeking clarification on the requirements of the problem.
Some participants mention issues with attachments that contain the original work, which may hinder the discussion. There is also a note about the requirement to prove the statement algebraically, which is central to the problem's constraints.
dx said:No, those arn't consecutive even integers. Just put x = 1, you get 2 and 3. 3 is not even.
HallsofIvy said:Ok, "two consectutive even numbers" can be represented as 2x and 2x+ 2. Now, what is the sum of their squares? What is the remainder of that number when divided by 8? And why did you label this "attempt at proof by contradiction" when there was no such attempt? And since the problem says "prove algebraically" I see no reason to even try proof by contradiction.