VWO 1993 Problem 3

For $a,b,c>0$ we have: $-1 < \left(\dfrac{a-b}{a+b}\right)^{1993} + \left(\dfrac{b-c}{b+c}\right)^{1993} + \left(\dfrac{c-a}{c+a}\right)^{1993} < 1$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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