Difference between revisions of "2014 USAMO Problems/Problem 6"
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Revision as of 18:09, 14 May 2014
Problem
Prove that there is a constant 
with the following property: If 
are positive integers such that 
for all 
, then![\[\min\{a, b\}>c^n\cdot n^{\frac{n}{2}}.\]](http://latex.artofproblemsolving.com/0/2/b/02b7074a6db67693e1ca47702b4fe57d70147d3a.png)
Solution
Without loss of generality, let 
.
