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: $2^3=8\equiv-1\pmod9$. $156221=3\cdot52073+2$.
Added: Since $7\equiv1\pmod 3$, $7^{18621}-1\equiv1^{18621}-1\equiv0\pmod3$.
