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Thorak

Two mathematicians

Question

There are two natural numbers greater than one, whose sum is less than 100.
And there are two friends: Peter, who knows the product of the numbers, and Paul, who knows their sum.
A following dialogue takes place:
Peter: "I don't know those numbers."
Paul: "I knew you wouldn't. I don't know them either."
Peter: "Now I know them!"
Paul: "Now I know them, too!"
What are those two numbers?

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