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GCD genius problem from our favorite author

Source: Kyiv City MO 2022 Round 2, Problem 9.1

January 30, 2022
number theorygreatest common divisor

Problem Statement

Find all triples (a,b,c)(a, b, c) of positive integers for which a+(a,b)=b+(b,c)=c+(c,a)a + (a, b) = b + (b, c) = c + (c, a).
Here (a,b)(a, b) denotes the greatest common divisor of integers a,ba, b.
(Proposed by Mykhailo Shtandenko)
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