How do I find a value for $ 2^{156221} - 1\pmod 9$? Again the problem is: Calculate the value of:
$$\left(2^{156221} - 1\right) \bmod 9$$
I have no idea how to find a solution to this and need help urgently!!
Thank you in advance.

Hint:  Have you tried just listing $2^1, 2^2, 2^3, \ldots \pmod 9$ for a while?  You might get some ideas.
