IMO 1979 LL USA63

If a1, a2, . . . , an denote the lengths of the sides of an arbitrary

imolonglistmathematicsolympiad

IMO 1979 LL USA63

Origin: USA

Problem

If a1, a2, . . . , an denote the lengths of the sides of an arbitrary n-gon, prove that 2 \geq a1 s −a1 + a2 s −a2

  • \cdot \cdot \cdot + an s −an \geq n n −1, where s = a1 + a2 + \cdot \cdot \cdot + an.