# Information disclosure puzzle

There are not many of my friends who expect me to spend a day pondering U2, but to stave off the boredom, I would like to pose to you a fascinating puzzle I came across the other day.

Two people, A and B, are told the sum of two integers and the sum of the squares of those two non-zero natural numbers respectively, and is told what the information they have been given is. Without lying, they have this discussion:

**B:** I do not know the numbers.

**A:** I do not know the numbers.

**B:** I do not know the numbers.

**A:** I do not know the numbers.

**B:** I do not know the numbers.

**A:** I do not know the numbers.

**B:** I know the numbers.

What are the two numbers?

To get the answer is quite easy (have fun), but to prove that it is the answer is really highly non-trivial, and I have not managed that yet.