points on a circle.
Source: Central American Olympiad 2001, problem 6
August 12, 2009
modular arithmetic
Problem Statement
In a circumference of a circle, points are marked, and they are numbered from to in a clockwise manner. segments are drawn in such a way so that the following conditions are met:
1. Each segment joins two marked points.
2. Each marked point belongs to one and only one segment.
3. Each segment intersects exactly one of the remaining segments.
4. A number is assigned to each segment that is the product of the number assigned to each end point of the segment.
Let be the sum of the products assigned to all the segments.
Show that is a multiple of .