Exhaustion

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Find the positive integer solutions of the equation

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

[Both this problem and the problem Proximity come from the Hungarian magazine KoMaL and you'll find many other challenging problems in English on the KoMal website ]
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Published September 2000.