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Find the positive integer solutions of the equation
 

\[ \left(1 + \frac{1}{a}\right)\left(1 + \frac{1}{b}\right) \left(1+ \frac{1}{c}\right) = 2. \]
 
 

This problem was taken from the Hungarian magazine KoMaL. There are many other challenging problems in English on the KoMal website.