2005 USAMO Problems/Problem 6
Revision as of 14:56, 30 March 2009 by FantasyLover (talk | contribs) (New page: ==Problem== For <math>m</math> a positive integer, let <math>s(m)</math> be the sum of the digits of <math>m</math>. For <math>n\ge 2</math>, let <math>f(n)</math> be the minimal <math>k</...)
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)
