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easy gcse maths question watch

1. ----
2. The two consecutive even integers can be written as 2n and 2n + 2.

Sum of squares
= (2n)^2 + (2n + 2)^2
= 4n^2 + 4n^2 + 8n + 4
= 8n^2 + 8n + 4
= 8(n^2 + n) + 4

Since n^2 + n is an integer, the sum of squares leaves a remainder 4 when divided by 8.

So the sum of squares is not a multiple of 8.
3. (Original post by Jonny W)
The two consecutive even integers can be written as 2n and 2n + 2.

Sum of squares
= (2n)^2 + (2n + 2)^2
= 4n^2 + 4n^2 + 8n + 4
= 8n^2 + 8n + 4
= 8(n^2 + n) + 4

Since n^2 + n is an integer, the sum of squares leaves a remainder 4 when divided by 8.

So the sum of squares is not a multiple of 8.
Yep, i just tried it, and did the exact same method (no point rewriting). This certainly doesnt seem like a GCSE question though...
4. Yeh perhaps a bit steep for gcse. Modular arithmetic eats it up without a second thought though.

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