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## Homework Statement

Prove that the difference between the equares of any two odd numbers is a multiple of 8.

## Homework Equations

n/a

## The Attempt at a Solution

where r is an integer, and n is an integer:

(2r-1)^2 - (2n-1)^2

4r^2 - 4r + 1 - 4n^2 + 4n - 1

4r^2 - 4r - 4n^2 + 4n

4(r^2 - r - n^2 + n)

now, that would show it to be multiple of 4, does this then suffice for proof for a multiple of 8? (8 a multiple of 4)

thnx, just need a quick confirmation of this..

cheers