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DE-BUNDESWETTBEWERB 2019 Problem 6

    Determine the smallest possible value of the sum S(a,b,c)=abc+bca+cabS (a, b, c) = \frac{ab}{c}+\frac{bc}{a}+\frac{ca}{b} where a,b,ca, b, c are three positive real numbers with a2+b2+c2=1a^2 + b^2 + c^2 = 1

    Dataset text AI-MO AoPS. Quoted with source.

    Official text: Bundeswettbewerb Mathematik 2019 official paper, page 1.

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