2020 OIM Problems/Problem 4

Problem

Prove that there exists a set $C$ of 2020 positive and distinct integers that simultaneously fulfills the following properties:

  • When we calculate the greatest common factor of every two elements of $C$, we obtain a list of numbers that are all different.
  • When you calculate the least common multiple of every two elements of $C$, you get a list of numbers that are all different.

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

Solution

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See also

OIM Problems and Solutions