IMO 2016 Shortlist A2

Find the smallest real constant C such that for any positive real numbers a1,a2,a3,a4 and a5 (not necessarily distinct),...

imomathematicsolympiadshortlistalgebra

IMO 2016 Shortlist A2

Category: Algebra

Problem

Find the smallest real constant C such that for any positive real numbers a1,a2,a3,a4 and a5 (not necessarily distinct), one can always choose distinct subscripts i,j,k and l such that ai aj − ak al ⩽ C.