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Help! Power amp impedance question

I'm in the market for a power amp but fairly new to how they work. Here's the gist:
I need a power amp that I'll be running into a cab rated at 4 ohms. I'll be running the power amp at bridged-mono. Does this mean that I need to run the amp at 8 ohms bridged? I've read a few pages on it, and my understanding is that the current and voltage double in bridged mode. So I could run one channel of the power amp (in stereo) at 4 ohms into my 4 ohm cab, but to bridge I need to run the power amp at 8 ohms bridged into my 4 ohm cab. Is this correct? Would running 4 ohms bridged mean I need to run a 2 ohm cab? Appreciate any help, I'm new to this.
 
How could I bridge that to a 4 ohm cab?
You plug it in. But you won't get 1600w into 4 ohms. It's only rated for 1,000w into 2 ohms. Into 4 ohms you may get 700w.

I've read a few pages on it, and my understanding is that the current and voltage double in bridged mode
They do not. You can double the voltage with series bridging, or you can double the current with parallel bridging. But you can't do both.