Let

_{n}C

_{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

_{2p}C

_{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. :)

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