Sieving by large integers and covering systems of congruences
نویسندگان
چکیده
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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ژورنال
عنوان ژورنال: Journal of the American Mathematical Society
سال: 2006
ISSN: 0894-0347,1088-6834
DOI: 10.1090/s0894-0347-06-00549-2