### Anton's Problem

Once there were 3 friends (Anton, Simon, Paul) chatting to each other
in a dining hall.

The following happened:

**Anton:**- I've chosen two natural numbers which are both greater
than 1. I'm going to tell Simon the sum and Paul the product of
these numbers.

Anton then gave Simon the sum and Paul the product, such that each of
our friends knew "his" number only but not the number of the other
friend.
**Anton:**- Now, can you guess the numbers which I have in mind?

Simon and Paul liked this sort of game. Their conversation was the
following:
**Simon:**- I don't know Anton's numbers.
**Paul:**- I don't know them either.
**Simon:**- Hey, now I know.
**Paul:**- Then I know them too.

A maths professor had observed this whole situation from the very
beginning.
He went to our friends and said:
**Professor:**- I know Anton's numbers, too!

Now, what are Anton's numbers?

September 1, 2009