Find all triples $(a, b, c)$ of positive integers for which $a + [a, b] = b + [b, c] = c + [c, a]$. Here $[a, b]$ denotes the least common multiple of integers $a, b$. (Proposed by Mykhailo Shtandenko)
Source: Kyiv City MO 2022 Round 2, Problem 8.1
Tags: number theory, least common multiple
Find all triples $(a, b, c)$ of positive integers for which $a + [a, b] = b + [b, c] = c + [c, a]$. Here $[a, b]$ denotes the least common multiple of integers $a, b$. (Proposed by Mykhailo Shtandenko)