Difference between revisions of "2012 IMO Problems/Problem 6"
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| + | ==Problem== | ||
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> | |
| − | + | ==Solution== | |
| + | {{solution}} | ||
| + | |||
| + | ==See Also== | ||
| + | |||
| + | {{IMO box|year=2012|num-b=5|after=Last Problem}} | ||
Latest revision as of 00:29, 19 November 2023
Problem
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)
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
See Also
| 2012 IMO (Problems) • Resources | ||
| Preceded by Problem 5 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Last Problem |
| All IMO Problems and Solutions | ||
