Problem

Source: China south east mathematical olympiad 2004 day2 problem 8

Tags: inequalities, algebra unsolved, algebra



Determine the number of ordered quadruples $(x, y, z, u)$ of integers, such that \[\dfrac{x-y}{x+y}+\dfrac{y-z}{y+z}+\dfrac{z-u}{z+u}>0 \textrm{ and } 1\le x,y,z,u\le 10.\]