2012 IMO Problems/Problem 6
Revision as of 11:44, 21 June 2018 by Illogical 21 (talk | contribs) (Created page with "Find all positive integers <math>n</math> for which there exist non-negative integers <math>a_1, a_2, \ldots, a_n</math> such that \[ \frac{1}{2^{a_1}} + \frac{1}{2^{a_2}} + \...")
Find all positive integers 
for which there exist non-negative integers 
such that
\[
\frac{1}{2^{a_1}} + \frac{1}{2^{a_2}} + \cdots + \frac{1}{2^{a_n}} =
\frac{1}{3^{a_1}} + \frac{2}{3^{a_2}} + \cdots + \frac{n}{3^{a_n}} = 1.
\]
[i]Proposed by Dusan Djukic, Serbia[/i]
