Exhaustion

Find the positive integer solutions of the equation (1+1/a)(1+1/b)(1+1/c) = 2

Problem

 

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.