Here's my attempt, and I'm not sure if it is even close to the right direction.
If $P(X>m+n|X>m)=P(X>n)$ then if F is the cumulative distribution function of X, we have \frac{P(X>m+n)}{P(X>m+n)+P(m
Is this even anything?
I was hoping to be able to show that this function must be something like $F(n)=1-(1-p)^n$ where $p$ is the probability of a success but I don't know how to do that. Is this a dead end? If so what would be a good way to attack this?