Olimpiada Nacional de Irán 2007 Problema A4

$ n_{1},n_{2},\dots$$ n_{i}\geq2$$ \epsilon_{1},\epsilon_{2},\dots$$ \epsilon_{i}\in\{1,2\}$\[ \sqrt[n_{1}]{\epsilon_{1}+\sqrt[n_{2}]{\epsilon_{2}+\dots+\sqrt[n_{k}]{\epsilon_{k}}}}\]$ (1,2]$$ \sqrt[n_{1}]{\epsilon_{1}+\sqrt[n_{2}]{\epsilon_{2}+\dots}}$$ x\in(1,2]$$ n_{1},n_{2},\dots\in\mathbb N$$ n_{i}\geq2$$ \epsilon_{1},\epsilon_{2},\dots$$ n_{i}\geq2$$ \epsilon_{i}\in\{1,2\}$$ x=\sqrt[n_{1}]{\epsilon_{1}+\sqrt[n_{2}]{\epsilon_{2}+\dots}}$

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