[0BW]Prerequisites:[0BS].Given \(x ∈ \mathbb {R}\) and \(N ∈ \mathbb {N}, N≥ 2\), prove that at least one element of the set \(\{ x, 2x, \ldots , (N-1)x\} \) is at most distance \(1/N\) from an integer, that is, there exist \(n,m∈ℤ\) with \(1≤ n≤ N-1\) such that \(|nx-m|≤ 1/N\).
