Abstract
By an exact covering of modulusm, we mean a finite set of liner congruencesx≡a i (modm i ), (i=1,2,...r) with the properties: (I)m i ∣m, (i=1,2,...,r); (II) Each integer satisfies precisely one of the congruences. Let α≥0, β≥0, be integers and letp andq be primes. Let μ (m) senote the Möbius function. Letm=p α q β and letT(m) be the number of exact coverings of modulusm. Then,T(m) is given recursively by
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References
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Friedlander, J. On exact coverings of the integers. Israel J. Math. 12, 299–305 (1972). https://doi.org/10.1007/BF02790756
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DOI: https://doi.org/10.1007/BF02790756