Math Induction Solution: Proving 5^(2n) - 1 is Divisible by 8

[Kinetica]

Homework Statement

Show

5^(2n) - 1 divisible by 8.

The Attempt at a Solution

For n =1, it is div. by 8.
For n=k+1,

5^(2(k+1)) - 1
=25^(k+1) - 1


I am not quite sure if this is the final solution.

 

[micromass]

Hi Kinetica!

Maybe you can start by factoring 5^{2n}-1.

 

[Kinetica]

Hey! I got it! Thanks!

5^[2(k+1)] - 1
25*5^[2k] - 1
5^[2k] + 24*5^[2k] - 1
5^[2k] - 1 + 24*5^[2k]