Congruence

**LegendWayne** · April 14th 2009, 05:38 AM

Find all integer solutions to
$-2^0-2^1-2^2-...-2^{q-1} \equiv 0 \bmod q^{p-1}$
Where
$2p \geq q$
$p$ is prime.

I know that the only solution is 1,1 (Using brute force through my graphing calculator)
This is actually part of another question in which I tried to solve and got stuck here. (I'm pretty sure what I've done before this is correct)
So if $p$ being prime is not used, it's alright.

**Media_Man** · April 15th 2009, 12:12 PM

Are these minus signs?

$<br /> -2^0-2^1-2^2-...-2^{q-1} \equiv 0 \bmod q^{p-1}<br />$

Then you are asking us to solve the congruence, given arbitrary q, find a prime $p \geq q/2$ such that: $q^{p-1}|2^q-1$

But you said the only solution is p=1,q=1, which is true, except that p is not prime.

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