Difference between revisions of "2005 USAMO Problems/Problem 6"
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==Solution== | ==Solution== | ||
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== See Also== | == See Also== | ||
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{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 20:52, 17 October 2013
Problem
For 
a positive integer, let 
be the sum of the digits of . For 
, let 
be the minimal 
for which there exists a set 
of 
positive integers such that 
for any nonempty subset 
. Prove that there are constants 
with
![\[C_1 \log_{10} n \le f(n) \le C_2 \log_{10} n.\]](http://latex.artofproblemsolving.com/7/3/7/73781eed2cabf9a48a7d376ce6846b3fb2b631f8.png)
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it. By Jason's theorem number 1239142, we know this is true.
See Also
| 2005 USAMO (Problems • Resources) | ||
| Preceded by Problem 5 |
Followed by Last Question | |
| 1 • 2 • 3 • 4 • 5 • 6 | ||
| All USAMO Problems and Solutions | ||
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. 
