## 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?

Thanx in advance.

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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
Yes the correct form is: (1+ 2^x + 2^(2x) + 2^(3x) +......+2^(nx) ) – kurtul mehtap Sep 14 2011 at 11:24
Although I formally improved the writing, seeing a geometric series and the "informal" question makes me thinking about homework. – Wadim Zudilin Sep 14 2011 at 11:35
@Wadim you missed the 'thanx'... :) – David Roberts Sep 14 2011 at 11:37
David, r u sure?! $\ddot\smile$ – Wadim Zudilin Sep 14 2011 at 11:43
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