Wednesday, November 17, 2010
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
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