Sum and Product
Two perfect logicians S and P are told that integers x and y are such that:
1 < x < y and that x + y < 100.
S and P are then given the values x+y and x*y respectively and privately. S and P know they have each been given the sum and product respectively. They then have the following conversation:
P: I cannot determine the two numbers.
S: I knew that.
P: Now I can determine them.
S: So can I.
Given that they spoke the truth, what are the two numbers?