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Omni-MATH / Find all integers n≥3 such that among any n positive real numbers a₁ , a₂ , … , a_(n) with max(a₁,a₂,…,a_(n))≤n⋅min(a₁,a₂,…,a_(n)), there exist three that are the side lengths of a…

Problem

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problem

Find all integers n≥3n \ge 3 such that among any nn positive real numbers a1a_1 , a2a_2 , …\dots , ana_n with max(a1,a2,…,an)≤n⋅min(a1,a2,…,an),\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.
Plain-text mathematical notation (without MathML)
Find all integers n≥3 such that among any n positive real numbers a₁ , a₂ , … , a_(n) with max(a₁,a₂,…,a_(n))≤n⋅min(a₁,a₂,…,a_(n)), there exist three that are the side lengths of an acute triangle.
Original LaTeX notation
Find all integers $n \ge 3$ such that among any $n$ positive real numbers $a_1$ , $a_2$ , $\dots$ , $a_n$ 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.

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Source and history

task_id
55193385-d311-5eb4-8257-bd43a4214f02
task_key
test--55193385-d311-5eb4-8257-bd43a4214f02
task_revision_id
1
config / split
/ test

Official source

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