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Covering the integers by arithmetic sequences

Covering the integers by arithmetic sequences

Let A = {as + nsZ} k=1 (n1 6 ··· 6 nk) be a system of arithmetic sequences where a1,··· ,ak 2 Z and n1,··· ,nk 2 Z + . For m 2 Z + system A will be called an (exact) m-cover of Z if every integer is covered …