EE-MO 2004

Find all pairs of real numbers $(x, y)$ that satisfy the equation $\frac{x + 6}{y}+\frac{13}{xy}=\frac{4-y}{x}$

The positive differences $a_i-a_j$ of five different positive integers $a_1, a_2, a_3, a_4, a_5$ are all different (there are altogether $10$ such differences). Find the least possible value of the largest number among the $a_i$ .

On the sides $AB , BC$ of the convex quadrilateral $ABCD$ lie points $M$ and $N$ such that $AN$ and $CM$ each divide the quadrilateral $ABCD$ into two equal area parts. Prove that the line $MN$ and $AC$ are parallel.