OK thank you, it's 'Polar Bear' than.
Reading you're answer made me think some minutes because remembering the brain cracking work I had with this riddle I couldn't imagine it to be solved so easily (and differing from my solution), and after reading my previous post over and over again I now have to seriously apologize for 2 major mistakes in the riddle as I wrote it down.
First of all I (shame on me) completely missed to say the integers are to be >1 (and <100 if that is for any help) so 1<a,b<100. I'm sorry.
The second and even worse thing is that I mixed up the order in which the Polar Bear and the Penguin appear.
The final and correct version of the riddle I sadly messed up
1. The Polar Bear is telling the Penguine: I know a product X which is calculated by the factors a and b so a*b=X , but I don't know what a and b are.
2. The Penguin says: I know a sum Y which is calculated by a and b so a+b=Y . I don't know which numbers a and b are, but I knew that you wouldn't know either.
3. The Polar Bear replies: Well if you say that, than I know the solution which numbers a and b are.
4. The Penguin says: OK, so if you say that, than I also know what a and b are.
I apologize for any inconvenience. :'(