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'Exhaustion' printed from https://nrich.maths.org/
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.