Many gcd's and lcm's
Source: 2020 Iberoamerican #4
November 17, 2020
number theory
Problem Statement
Show that there exists a set of distinct, positive integers that satisfies simultaneously the following properties:
When one computes the greatest common divisor of each pair of elements of , one gets a list of numbers that are all distinct.
When one computes the least common multiple of each pair of elements of , one gets a list of numbers that are all distinct.