Use mathematical induction.Originally Posted byTatanka

Set x_n = 3^(2n+2) -8n -9.

Solve for the power term on the right:

x_n + 8n + 9 = 3^(2n+2)

Now look at the term for the next n:

x_n+1 = 3^(2n+4) -8(n+1) - 9

= 9*3^(2n+2) - 8n - 17

= 9*(x_n + 8n + 9) -8n - 17

= ...

Use this to prove that if x_n is divisible by 64, x_n+1 is divisible by 64 as well.

You still need to start the induction for some n:-)