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.