tough logic problem

[wins_pot]

Two integers, m and n, each between 2 and 100 inclusive, have been
chosen. The product, mn, is given to mathematician X. The sum, m + n,
is given to mathematician Y. Their conversation is as follows:

X: I don't have the foggiest idea what your sum is, Y.

Y: That's no news to me, X. I already knew that you didn't
know.

X: Aha, NOW I know what your sum must be, Y!

Y: And likewise X, I have surmised your product!

Find the integers m and n.

can you prove uniquenss? (i can't. don't even know if it's possible)