11th Iberoamerican Mathematical Olympiad Problems 1996

A1.  Find the smallest positive integer n so that a cube with side n can be divided into 1996 cubes each with side a positive integer. A2.  M is the midpoint of the median AD of the triangle ABC. The ray BM meets AC at N. Show that AB is tangent to the circumcircle of NBC iff BM/MN = (BC/BN)2.