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Found problems: 1

2015 Bosnia and Herzegovina Junior BMO TST, 2
Tags: solve , triplets , number theory
Find all triplets of positive integers $a$, $b$ and $c$ such that $a \geq b \geq c$ and $\left(1+\frac{1}{a}\right)\left(1+\frac{1}{b}\right)\left(1+\frac{1}{c}\right)=2$