Difference between revisions of "2021 USAMO Problems/Problem 4"
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==Problem== | ==Problem== | ||
| − | A finite set <math>S</math> of positive integers has the property that, for each <math>s\in S</math>, and each positive integer <math>d</math> of <math>s</math>, there exists a unique element <math>t \in S</math> satisfying <math>\gcd(s,t)=d</math> (the elements <math>s</math> and <math>t</math> could be equal). | + | 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>, there exists a unique element <math>t \in S</math> satisfying <math>\gcd(s,t)=d</math> (the elements <math>s</math> and <math>t</math> could be equal). |
Given this information, find all possible values for the number of elements of <math>S</math>. | Given this information, find all possible values for the number of elements of <math>S</math>. | ||
Latest revision as of 12:59, 3 March 2023
Problem
A finite set 
of positive integers has the property that, for each 
, and each positive integer divisor 
of 
, there exists a unique element 
satisfying 
(the elements and 
could be equal).
Given this information, find all possible values for the number of elements of .
