Mathematics Professor Pierre Marchand at Univ of Nancy, France 
told me this one.

There are two integers x,y between 2 and 100, inclusive, and
two people P,S.  P is told the product x*y.  S is told the
sum x+y.  Neither is told the specific values of x,y. 
P,S have the following conversation:

   S:  I cannot determine x,y.
   P:  I cannot determine x,y.
   S:  I already knew that.
   P:  In that case, I now know x,y.
   S:  In that case, I too now know x,y.

What are x,y?  (and how long did it take to solve?)