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Irreducible disjoint covering systems of \({\mathbb{Z}}\) with the common modulus consisting of three primes. (English) Zbl 0612.10002
A system of k congruence classes \(a_ i\) (mod \(n_ i)\), \(1\leq i\leq k\), is called disjoint covering if every integer belongs exactly to one of these classes. A disjoint covering system is said to be irreducible (IDCS) if the union of none of its non-trivial subsystems is a congruence class. The paper deals with IDCS’s in which the l.c.m. of all the moduli is the product of three distinct primes. The author proves a structural result and gives an upper and lower bound for the so-called Mycielski abundance of such IDCS’s.
Reviewer: Št.Porubský

11A07 Congruences; primitive roots; residue systems
11B25 Arithmetic progressions