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Attempt at proof by contradiction need verification

  • #1

Homework Statement


GCSE past paper question.
prove algebraically that the sum of the squares of any two consecutive even integers is never a multiple of 8


Homework Equations



none

The Attempt at a Solution



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

see attachment.
 

Attachments

Last edited:

Answers and Replies

  • #2
dx
Homework Helper
Gold Member
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No, those arn't consecutive even integers. Just put x = 1, you get 2 and 3. 3 is not even.
 
  • #3
alternative non word attachment, mathematica
 

Attachments

  • #4
No, those arn't consecutive even integers. Just put x = 1, you get 2 and 3. 3 is not even.
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:
  • #5
HallsofIvy
Science Advisor
Homework Helper
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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.
 
  • #6
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.
see microsoft word attatchment or mathmatica attatchment for the attempt. for a contridiction i made the sum equal to the multiple of 8.
 
  • #7
HallsofIvy
Science Advisor
Homework Helper
41,792
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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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