The Puzzle Thread

[leonid]

Here's one of my favorite math puzzles:

Me: Here are integers A and B, both greater than 1. Bob is given AxB and Sam is given A+B.
Me: Bob, do you know what A and B are?
Bob: I don't know.
Me: Bob doesn't know. What about you, Sam?
Sam: I don't know, either.
Bob: Ah! I know what they are.
Sam: I as well know what they are.

What are A and B?

EDIT: Let's just say A<=B to prevent confusion