# Attempt at proof by contradiction need verification

## 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

none

## The Attempt at a Solution

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

see attachment.

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dx
Homework Helper
Gold Member
No, those arn't consecutive even integers. Just put x = 1, you get 2 and 3. 3 is not even.

alternative non word attachment, mathematica

#### Attachments

• Untitled-1.nb
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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:
HallsofIvy
Homework Helper
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.

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.

HallsofIvy