Moldova City Olympiad 2008.

Here are the problems for the 12th grade. I will try to post the problems for other grades soon. The problems are rather easy, for beginners mainly. However when I find time, I will try to provide their solutions.
Moldova, Chisinau, City Olympiad 2008, February 23.
Grade 12.
Problem 1.
The polynomial takes integer values for . Prove [...]