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 upsilon(1), ..., upsilon(n) there is a real number x such that each \\upsilon(i)x\\ greater than or equal to (n+l)(-1) (here \\y\\ denotes the distance from y to the nearest integer). This conjecture has been previously solved for n less than or equal to 4. In this paper we prove that when 2n-3 is a prime and n greater than or equal to 4 we can find a real number a which gives each \\upsilon(i)x\\ greater than or equal to 1/(2n - 3). In fact more than this is proved. (C) 1999 Academic Press.