2005 USAMO Problems/Problem 6: Difference between revisions
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C_1 \log_{10} n \le f(n) \le C_2 \log_{10} n. | C_1 \log_{10} n \le f(n) \le C_2 \log_{10} n. | ||
</cmath> | </cmath> | ||
==Solution== | |||
{{solution}} | |||
== See Also== | |||
{{USAMO newbox|year=2005|num-b=5|after=Last Question}} | |||
Revision as of 18:05, 11 April 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
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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 | ||
