2021 USAMO Problems/Problem 4

Revision as of 13:22, 15 September 2021 by Dneary (talk | contribs) (Change to the actual Q4)

Problem

A finite set $S$ of positive integers has the property that, for each $s\in S$, and each positive integer $d$ of $s$, there exists a unique element $t \in S$ satisfying $\gcd(s,t)=d$ (the elements $s$ and $t$ could be equal).

Given this information, find all possible values for the number of elements of $S$.