24th All Russian Mathematical Olympiad Problems 1998

1.  a and b are such that there are two arcs of the parabola y = x2 + ax + b lying between the ray y = x, x > 0 and y = 2x, x > 0. Show that the projection of the left-hand arc onto the x-axis is smaller than the projection of the right-hand arc by 1. 2.  A convex polygon is partitioned into parallelograms, show that at least three vertices of the polygon belong to