منابع مشابه
Sieving by Large Integers and Covering Systems of Congruences
An old question of Erdős asks if there exists, for each number N , a finite set S of integers greater than N and residue classes r(n) (mod n) for n ∈ S whose union is Z. We prove that if ∑ n∈S 1/n is bounded for such a covering of the integers, then the least member of S is also bounded, thus confirming a conjecture of Erdős and Selfridge. We also prove a conjecture of Erdős and Graham, that, f...
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متن کاملBesicovitch Covering Property for Homogeneous Distances on the Heisenberg Groups
We prove that the Besicovitch Covering Property (BCP) holds for homogeneous distances on the Heisenberg groups whose unit ball centered at the origin coincides with an Euclidean ball. We provide therefore the first examples of homogeneous distances that satisfy BCP in these groups. Indeed, commonly used homogeneous distances, such as (Cygan-)Korányi and Carnot-Carathéodory distances, are known ...
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ژورنال
عنوان ژورنال: Rocky Mountain Journal of Mathematics
سال: 1997
ISSN: 0035-7596
DOI: 10.1216/rmjm/1181071965