A rational Beatty sequence is a set of integers of the form \([\alpha +nr]\) with n running over the set \({\mathbb{Z}}^+\) if nonnegative integers and \(\alpha\) a real and r a rational number with \(n\geq 1\). Here [ ] denotes the greatest integer function and r is called the modulus of the sequence.
The authors prove that if a finite system of Beatty sequences partitions \({\mathbb{Z}}^+\) then the greatest among the numerators of the moduli (written in their lowest terms) of these sequences appears at least twice. This is a generalization of the well known result of Davenport, Mirsky, D. Newman and Rado for disjoint covering systems of arithmetic sequences. They also prove that even three largest numerators are equal provided the system contains at least three sequences and the moduli corresponding to these numerators are not equal.