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an algebra and inequality problem

Source: China south east mathematical olympiad 2004 day2 problem 8

June 29, 2013
inequalitiesalgebra unsolvedalgebra

Problem Statement

Determine the number of ordered quadruples (x,y,z,u)(x, y, z, u) of integers, such that x−yx+y+y−zy+z+z−uz+u>0 and 1≤x,y,z,u≤10.\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.
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