2nd Chinese Mathematical Olympiad 1987 Problems & Solutions

A1.  n is a positive integer. Show that zn+1 - zn - 1 = 0 has a root on the unit circle |z| = 1 iff n is congruent to 4 mod 6. A2.  An equilateral triangle side n is divided into n2 equilateral triangles of side 1 by lines parallel to its sides. The n(n+1)/2 vertices of the triangles are each labeled with a real number, so that if ABC and BCD are small triangles then the sum