IMO 1989 LL VIE111

Origin: VIE

Problem

Find the greatest number c such that for all natural numbers n, {n \sqrt 2} \geqc n (where {n \sqrt 2} = n \sqrt 2 −[n \sqrt 2]; [x] is the integer part of x). For this number c, find all natural numbers n for which {n \sqrt 2} = c n.