IMO 2012: Day 2 Problem 6
Posted: Thu Jul 12, 2012 1:19 am
Find all positive integers $n$ for which there exist non-negative integers $a_1,a_2,\cdots, a_n$ such that \[\frac{1}{2^{a_1}}+\frac{1}{2^{a_2}}+\cdots+\frac{1}{2^{a_n}}=\frac{1}{3^{a_1}}+\frac{2}{3^{a_2}}+\cdots+\frac{n}{3^{a_n}}=1\]
