Find all triples of pairwise distinct positive integers $(a,b,c)$, which satisfy the following conditions: $2a-1$ is divisible by $b$, $2b-1$ is divisible $c$ and $2c-1$ is divisible by $a$. Proposed by Bohdan Rublyov
Source: Ukrainian mathematical olympiad 2018 11.1
Tags: number theory
Find all triples of pairwise distinct positive integers $(a,b,c)$, which satisfy the following conditions: $2a-1$ is divisible by $b$, $2b-1$ is divisible $c$ and $2c-1$ is divisible by $a$. Proposed by Bohdan Rublyov