Proving Divisibility of (n^2-1) for Odd Integers n

[scott_bruenin]

Homework Statement

For each integer n, if n is odd then 8\left| (n^{2}-1)

Homework Equations

Def of an odd number 2q+1

The Attempt at a Solution

(2q+1)^{2} -1
4q^{2} +4q+1-1
4q^{2} +4q
Here is where I get stuck... should I factor out the 4 and say that q^{2} +q is an integer and therefore can be wrote as some integer r and therefore 8\left| 4r?

 

[Dick]

Can you show q^2+q is divisible by 2 for any integer q? If so, then 4q^2+4q is divisible by 8.