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IMO-2012 Problem 6 (Dušan Djukić, Serbia)  

Find all positive integers ( n ) for which there exist non-negative integers ${a_1}$, $a_2 $, $ \dots $, $ a_n $ such that \[ \frac1{2^{a_1}}+\frac1{2^{a_2}}+\cdots+\frac1{2^{a_n}}=\frac1{3^{a_1}}+\frac2{3^{a_2}}+\cdots+\frac{n}{3^{a_n}}=1.\]

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