LHIRT POD #3

It's time for a little number theory for the POD:

Let _nC_r be the number of ways to choose r items from n objects (or "n choose r"). Assume p is prime. Determine what the remainder of _2pC_p divided by p is, and prove it. For extra credit, is the converse true?

This one may be a little tough if you don't see it off the bat, so I'll leave it up for a while. Besides, I'm not entirely sure about the converse part myself. :)