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Bosnia and Herzegovina JBMO TST 2015 Problem 2

Source: Bosnia and Herzegovina Junior Balkan Mathematical Olympiad TST 2015

September 16, 2018

number theorysolvetriplets

Problem Statement

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