IMO 1984 SL 1

Origin: FRA

Problem

Find all solutions of the following system of n equations in n variables: x1|x1| −(x1 −a)|x1 −a| = x2|x2|, x2|x2| −(x2 −a)|x2 −a| = x3|x3|, \cdot \cdot \cdot xn|xn| −(xn −a)|xn −a| = x1|x1|, where a is a given number.

Solution

This is the same problem as (SL83-20).