Question 2
Find all integers $n \ge 3$ such that among any $n$ positive real numbers
$a_1$, $a_2$, …, $a_n$ with
\[\max(a_1,a_2,\dots,a_n)
\le n \cdot \min(a_1,a_2,\dots,a_n),\]
there exist three that are the side lengths of an acute triangle.
Proposed by Titu Andreescu (credit in the supplied notes).
$a_1$, $a_2$, …, $a_n$ with
\[\max(a_1,a_2,\dots,a_n)
\le n \cdot \min(a_1,a_2,\dots,a_n),\]
there exist three that are the side lengths of an acute triangle.
Proposed by Titu Andreescu (credit in the supplied notes).