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Omni-MATH / A finite set S of positive integers has the property that, for each s∈S, and each positive integer divisor d of s , there exists a unique element t∈S satisfying gcd(s,t)=d . (The e…

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problem

A finite set SS of positive integers has the property that, for each s∈S,s \in S, and each positive integer divisor dd of ss , there exists a unique element t∈St \in S satisfying gcd(s,t)=d\text{gcd}(s, t) = d . (The elements ss and tt could be equal.) Given this information, find all possible values for the number of elements of SS .
Plain-text mathematical notation (without MathML)
A finite set S of positive integers has the property that, for each s∈S, and each positive integer divisor d of s , there exists a unique element t∈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 .
Original LaTeX notation
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 $S$ .

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Source and history

task_id
4fbc320f-d6e1-503e-9e56-88ab63b6a149
task_key
test--4fbc320f-d6e1-503e-9e56-88ab63b6a149
task_revision_id
1
config / split
/ test

Official source

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