3rd Iberoamerican Mathematical Olympiad Problems 1988

A1.  The sides of a triangle form an arithmetic progression. The altitudes also form an arithmetic progression. Show that the triangle must be equilateral. A2.  The positive integers a, b, c, d, p, q satisfy ad - bc = 1 and a/b > p/q > c/d. Show that q ≥ b + d and that if q = b + d, then p = a + c.