Managed to solve this by hand but I think it was designed to be done by computer

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

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

Find the integers m and n.