IMO Shortlist 2012 problem N7
Dodao/la:
arhiva3. studenoga 2013. Find all positive integers
for which there exist non-negative integers
such that
Proposed by Dusan Djukic, Serbia
%V0
Find all positive integers $n$ for which there exist non-negative integers $a_1, a_2, \ldots, a_n$ such that
$$\frac{1}{2^{a_1}} + \frac{1}{2^{a_2}} + \cdots + \frac{1}{2^{a_n}} = \frac{1}{3^{a_1}} + \frac{2}{3^{a_2}} + \cdots + \frac{n}{3^{a_n}} = 1\text{.}$$
Proposed by Dusan Djukic, Serbia
Izvor: Međunarodna matematička olimpijada, shortlist 2012
Školjka 
