Difference between revisions of "2012 IMO Problems/Problem 6"
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}} + \...") |
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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 | 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 | ||
| − | + | <cmath> | |
\frac{1}{2^{a_1}} + \frac{1}{2^{a_2}} + \cdots + \frac{1}{2^{a_n}} = | \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. | \frac{1}{3^{a_1}} + \frac{2}{3^{a_2}} + \cdots + \frac{n}{3^{a_n}} = 1. | ||
| − | + | </cmath> | |
| − | + | Proposed by Dusan Djukic, Serbia | |
Revision as of 11:46, 21 June 2018
Find all positive integers 
for which there exist non-negative integers 
such that
![\[\frac{1}{2^{a_1}} + \frac{1}{2^{a_2}} + \cdots + \frac{1}{2^{a_n}} = \frac{1}{3^{a_1}} + \frac{2}{3^{a_2}} + \cdots + \frac{n}{3^{a_n}} = 1.\]](http://latex.artofproblemsolving.com/b/0/f/b0fa90026dcd8289f99183337e2bfd121077dd0f.png)
Proposed by Dusan Djukic, Serbia
