1st Austrian-Polish Mathematics Competition 1978 Problems

1st Austrian-Polish Mathematics Competition 1978 Problems1.  Find all real-valued functions f on the positive reals which satisfy f(x + y) = f(x2 + y2) for all positive x, y. 2.  A parallelogram has its vertices on the boundary of a regular hexagon and its center at the center of the hexagon. Show that its area is at most 2/3 the area of the hexagon.