## Congruence of a power series [closed]

Dear All,

I need to find the result of $1+ 2^x + 2^{2x} + 2^{3x} +\dots+2^{nx} \pmod {2^{x-3}-7 }$. Is there a short way of finding it instead of calculating $\pmod{ 2^{x-3}-7 }$ "$n-1$" times?

It looks like you may need some parentheses in your first expression. Is the $x$ in $nx$ in the exponent? – S. Carnahan Sep 14 2011 at 11:19
David, r u sure?! $\ddot\smile$ – Wadim Zudilin Sep 14 2011 at 11:43