منابع مشابه
Nearly Disjoint Covering Systems
We pose the problem of the existence of incongruent covering systems of residue sets, where two residue sets intersect if and only if their moduli are relatively prime . We show how such covering systems give rise to nearly disjoint cell covers of a lattice box, and thereby obtain a partial solution . In particular, we show that the number of primes dividing the 2 .c .m . of the moduli of the r...
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Let the collection of arithmetic sequences {din+ bi : n ∈ Z}i∈I be a disjoint covering system of the integers. We prove that if di = pq for some primes p, q and integers k, l ≥ 0, then there is a j 6= i such that di|dj . We conjecture that the divisibility result holds for all moduli. A disjoint covering system is called saturated if the sum of the reciprocals of the moduli is equal to 1. The a...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 1984
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-44-4-389-395