Edexcel Nov 2005 paper 5 ....

[SusanS]

I'm doing this paper at the mo. I can't do this question. I hate these odd, even number type questions. Where do i start?

Prove algebraically that the sum of the squares of any two odd numbers leaves a remainder of 2 when divided by 4.

[Unregistered]

Let the two odd numbers be (2m+1) and (2n+1)

The sum of their squares is (2m+1)^2 + (2n+1)^2

(2m+1)^2 + (2n+1)^2 = 4m^2 + 4m +1 + 4n^2 + 4n + 1
=4(m^2 + m + n^2 + n) + 2
=4k + 2 where k is an integer (whole number)

Hence the remainder when divided by 4 will always be 2

[SusanS]

Thanks for the help. :)