Proving the Divisibility of 8 and Odd Squares

[PennState666]

Prime Division HELP!

Homework Statement

I need to be able to understand and likely prove that for any positive odd integer n,
8 | (n^2 -1 )

Homework Equations

The Attempt at a Solution

odd can be said to be n = 2k +1
so 8 | (2k + 1)^2 -1

 

[phyzguy]

Keep going. Now expand out (2k+1)^2 - 1 and collect terms. Then think about the terms in k and k+1.

 

[PennState666]

I got stumped trying mathematical induction i was hoping for a new approach

 

[Mark44]

Try the approach that phyzguy is suggesting.