Question 4
A finite set $S$ of positive integers has the property that for every $s\in S$ and positive divisor $d$ of $s$, exactly one $t\in S$ satisfies $\gcd(s,t)=d$; $s=t$ is allowed. Find all possible cardinalities of $S$.
Proposed by Carl Schildkraut. Evan Chen’s third-party solution notes: https://aops.com/community/p21498580; source video https://youtu.be/9WNgDETHOlI?t=1008. One point is nonofficial editorial normalization; manual essay grading only.
Proposed by Carl Schildkraut. Evan Chen’s third-party solution notes: https://aops.com/community/p21498580; source video https://youtu.be/9WNgDETHOlI?t=1008. One point is nonofficial editorial normalization; manual essay grading only.