Let A be a matrix of integers, and b a vector of integers such that all elements of b have a common divisor k. When does the polyhedron P(A,b)={x•x≥0,Ax•b} have integral extreme points only? The paper gives a necessary and sufficient condition for this to happen and provides its special version for the case where k is a prime number. For k=2, it gives applications, including a new result for the obnoxious facility location problem.
