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2014 BMT Spring
8
BMT 2014 Spring - Discrete 8
BMT 2014 Spring - Discrete 8
Source:
January 6, 2022
Problem Statement
Suppose that positive integers
a
1
,
a
2
,
…
,
a
2014
a_1,a_2,\ldots,a_{2014}
a
1
,
a
2
,
…
,
a
2014
(not necessarily distinct) satisfy the condition that:
a
1
a
2
,
a
2
a
3
,
…
,
a
2013
a
2014
\frac{a_1}{a_2},\frac{a_2}{a_3},\ldots,\frac{a_{2013}}{a_{2014}}
a
2
a
1
,
a
3
a
2
,
…
,
a
2014
a
2013
are pairwise distinct. What is the minimal possible number of distinct numbers in
{
a
1
,
a
2
,
…
,
a
2014
}
\{a_1,a_2,\ldots,a_{2014}\}
{
a
1
,
a
2
,
…
,
a
2014
}
?
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