27th International Mathematical Olympiad 1986 Problems & Solutions

A1.  Let d be any positive integer not equal to 2, 5 or 13. Show that one can find distinct a, b in the set {2, 5, 13, d} such that ab - 1 is not a perfect square. A2.  Given a point P0 in the plane of the triangle A1A2A3. Define As = As-3 for all s >= 4. Construct a set of points P1, P2, P3, ... such that Pk+1 is the image of Pk under a rotation center Ak+1 through an angle