  A commutative ring R is said to be coverable if it is the union of its proper
subrings and said to be finitely coverable if it is the union of a finite
number of them. In the latter case, we denote by {\sigma}(R) the minimal number
of required subrings. In this paper, we give necessary and sufficient
conditions for the ring of integers A of a given number field to be finitely
coverable and a formula for {\sigma}(A) is given which holds when they are met.
The conditions are expressed in terms of the existence of common index divisors
and (or) common divisors of values of polynomials.
