2010 OIM Problems/Problem 4
Problem
The arithmetic, geometric and harmonic means of two different positive integers are integer numbers. Find the smallest possible value for the arithmetic mean.
Note: If 
and 
are positive numbers, their arithmetic, geometric and harmonic means are, respectively: 
, 
, and $\frac{2ab}{a+b}.
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
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