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Attempt at proof by contradiction need verification

  1. May 13, 2008 #1
    1. The problem statement, all variables and given/known data
    GCSE past paper question.
    prove algebraically that the sum of the squares of any two consecutive even integers is never a multiple of 8

    2. Relevant equations


    3. The attempt at a solution

    n and x are integers 2x and 2x+2 represent two consecutive even integers.

    see attachment.

    Attached Files:

    Last edited: May 13, 2008
  2. jcsd
  3. May 13, 2008 #2


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    Homework Helper
    Gold Member

    No, those arn't consecutive even integers. Just put x = 1, you get 2 and 3. 3 is not even.
  4. May 13, 2008 #3
    alternative non word attachment, mathematica

    Attached Files:

  5. May 13, 2008 #4
    sorry should be 2x+2

    i will edit the post

    the document workings are as 2x+2

    further help would be appreciated thanks
    Last edited: May 13, 2008
  6. May 14, 2008 #5


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    Staff Emeritus
    Science Advisor

    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.
  7. May 17, 2008 #6
    see microsoft word attatchment or mathmatica attatchment for the attempt. for a contridiction i made the sum equal to the multiple of 8.
  8. May 17, 2008 #7


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    Staff Emeritus
    Science Advisor

    When I try to open the word attachment I see letters covered by black rectangles. I don't have mathematica so I can't open that. I don't see any reason to use "contradiction". Are you required to prove it that way?
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