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USAJMO problem 2: Side lengths of an acute triangle

Source: Also USAMO problem 1

April 24, 2012
USA(J)MOUSAMO2012 USAJMO2012 USAMOgeometryFibonacciinequalities

Problem Statement

Find all integers n≥3n \geq 3 such that among any nn positive real numbers a_1, a_2, \hdots, a_n with \text{max}(a_1,a_2,\hdots,a_n) \leq n \cdot \text{min}(a_1,a_2,\hdots,a_n), there exist three that are the side lengths of an acute triangle.
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