Abstract
We show that any m×m matrix M with integer entries and detM=Δ≠0 can be equipped by a finite digit set D⊂Zm such that any integer m-dimensional vector belongs to the setFinD(M)={∑k∈IMkdk:∅≠I finite subset of Z and dk∈D for each k∈I}⊂⋃k∈N1ΔkZm. We also characterize the matrices M for which the sets FinD(M) and ⋃k∈N1ΔkZm coincide.
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