# Homework Help: Help with proof using cases

1. Mar 10, 2008

### scott_bruenin

1. The problem statement, all variables and given/known data
For each integer n, if n is odd then 8$$\left|$$ (n$$^{2}$$-1)

2. Relevant equations
Def of an odd number 2q+1

3. 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?

2. Mar 10, 2008

### 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.