Difference between revisions of "2021 USAJMO Problems/Problem 5"

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[[Category:Olympiad Number Theory Problems]]
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Revision as of 13:24, 16 April 2021

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

See Also

2021 USAJMO (ProblemsResources)
Preceded by
Problem 3
Followed by
Problem 5
1 2 3 4 5 6
All USAJMO Problems and Solutions

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