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IMO 2012 NO 6

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Cari semua bilangan bulat positif $n$ yang mana terdapat bilangan bulat non-negatif $a_1$, $a_2$, $a_3$, ... , $a_n$ sehingga


$\displaystyle\sum\limits_{i=1}^n \displaystyle\frac{1}{2^{a_i}} = \displaystyle\sum\limits_{j=1}^n \displaystyle\frac{j}{3^{a_j}} = 1$

Edited by Zekrom

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