SILK-ROAD 2007 Problem 3

Find the max. value of $M$ ,such that for all $a,b,c>0$ : $a^{3}+b^{3}+c^{3}-3abc\geq M(|a-b|^{3}+|a-c|^{3}+|c-b|^{3})$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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