The view-obstruction problem for \(n\)-dimensional cubes
The view-obstruction problem for the \(n\)-dimensional cube is equivalent to the conjecture that for any \(n\) positive integers \(v_1,\dots, v_n\) there is a real number \(x\) with \[ \| v_ix\|\geq (n+1)^{-1}, \quad i=1,\dots, n, \] where \(\| y\|\) denotes the distance from \(y\) to the next integer. This conjecture has been previously solved for \(n=4\). The authors prove for \(p=2n-3\) prime and \(n\geq 4\) that there is a real \(x\) with \(\| v_ix\|\geq p^{-1}\), \(i=1,\dots, n\). Some further related results are given.
scientific article; zbMATH DE number 1271769
scientific article