IMO 1979 LL ROM56

Show that for every natural number n, n

imolonglistmathematicsolympiad

IMO 1979 LL ROM56

Origin: ROM

Problem

Show that for every natural number n, n \sqrt 2 −[n \sqrt 2] > 2n \sqrt and that for every \epsilon > 0 there exists a natural number n with n \sqrt 2 − [n \sqrt 2] < 2n \sqrt 2 + \epsilon.