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2003 Romania National Olympiad, 2

Let be eight real numbers $ 1\le a_1< a_2< a_3< a_4,x_1<x_2<x_3<x_4. $ Prove that $$ \begin{vmatrix}a_1^{x_1} & a_1^{x_2} & a_1^{x_3} & a_1^{x_4} \\ a_2^{x_1} & a_2^{x_2} & a_2^{x_3} & a_2^{x_4} \\ a_3^{x_1} & a_3^{x_2} & a_3^{x_3} & a_3^{x_4} \\ a_4^{x_1} & a_4^{x_2} & a_4^{x_3} & a_4^{x_4} \\ \end{vmatrix} >0. $$ [i]Marian Andronache, Ion Savu[/i]

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