Moldova, Third Team Selection Test for IMO and BMO 2008, March 30.

The pdf file is here.
Moldova, Third Team Selection Test for IMO-BMO 2008, March 30
Problem 1
Determine a subset having exactly distinct elements, whose sum of squares equals their product.
Problem 2
Let be a prime number and positive integers so that . Prove that and are coprime.
Problem 3
In triangle the bisector of [...]