RMO 2016

Algebra Level 3

Let \(a,b\) and \(c\) be 3 distinct positive numbers such that their product is 1. Find the infimium value of

\[ \dfrac{a^3}{(a-b)(a-c)} + \dfrac{b^3}{(b-c)(b-a)} + \dfrac{c^3}{(c-a)(c-b)} . \]

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