Find all pairs $a, b$ of positive integers, for which $$(a, b) + 3[a, b] = a^3 - b^3$$ Here $(a, b)$ denotes the greatest common divisor of $a, b$, and $[a, b]$ denotes the least common multiple of $a, b$. Proposed by Oleksiy Masalitin
Problem
Source: Ukrainian Mathematical Olympiad 2024. Day 1, Problem 11.1
Tags: greatest common divisor, least common multiple, number theory