v. on a conjecture of mahler
Published online by Cambridge University Press: 24 October 2008
Introduction. If ξ is a real number we denote by ∥ ξ ∥ the difference between ξ and the nearest integer, i.e.
It is well known (e.g. Koksma (3), I, Satz 4) that if θ1, θ2, …, θn are any real numbers, the inequality
has infinitely many integer solutions q > 0. In particular, if α is any real number, the inequality
has infinitely many solutions.