Oh dear, now this is embarrassing...

When the clock struck midnight, January 1, 2001, I was playing Super Mariokart with my roommate Tong. That's somewhat less exciting than last year's lightsuit fiesta...

The good news is that I won, via a triumphant use of the lightning bolt. So I guess that's sorta festive...

OK, now everything is better. I was feeling bad about my lack of a cool new year's event... so I got myself engaged in a high-level math discussion with Tong's math department grad student friends.

Holy crap, these guys are thinking on another plane of existance. I am struggling to wrap my measily brain around the concepts they're throwing around. My brain hurts. But here's a good logic puzzle that we just went over:

There are two integers, greater than one, A and B. Mr. Sum knows the value of S=A+B, Mr. Product knows the value of P=A*B. The following conversation ensues:

Mr. Sum: You cannot know what A and B are.

Mr. Product: OK, I now know the value of A and B.

Based on this dialogue, what are the smallest possible values for A and B? Bonus Question: Is there a unique solution for A and B?

This may seem like a silly question, but the math required to reach the solution just floored me. I am in awe of this question.