Zaimi-Marku inequality

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In mathematics, the Zaimi-Marku inequality goes as follows: Let a1,...,an be positive reals and k a real number. Then

(n-1)\sum_{i=1}^na_i^{n+k}+\prod_{i=1}^n a_i\sum_{i=1}^n a_i^k\geq \sum_{i=1}^n a_i\sum_{i=1}^na_i^{n+k-1}.

The Zaimi-Marku inequality was a product of the work of two young Albanians, Gjergji Zaimi and Keler Marku. They proved this inequality in June 2006, when they were only 17 years old.

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