olymmath

OSN 2013 Problem 3

    Determine all positive real MM such that for any positive reals a,b,ca,b,c , at least one of a+Mab,b+Mbc,c+Mcaa + \dfrac{M}{ab}, b + \dfrac{M}{bc}, c + \dfrac{M}{ca} is greater than or equal to 1+M1+M .

    Dataset text AI-MO AoPS. Quoted with source.

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