2021 USAJMO Problems/Problem 5

Revision as of 14:46, 15 April 2021 by Problemsolver2048 (talk | contribs) (Created page with "A finite set <math>S</math> of positive integers has the property that, for each <math>s \in S,</math> and each positive integer divisor <math>d</math> of <math>s</math>, ther...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

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

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

Solution