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An extremal problem for least common multiples

✍ Scribed by Melvyn B Nathanson

Publisher: Elsevier Science
Year: 1987
Tongue: English
Weight: 482 KB
Volume: 64
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(87)90191-9

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✦ Synopsis

Let A be a set of natural numbers, and let [A] h denote the set of all least common multiples [al .... , ah] with ai ~ A. If n ¢ [A] h for all sufficiently large integers n, then A is an asymptotic LCM basis of order h. If n ¢ [A] h for infinitely many n t> 1, then A is an asymptotic LCM nonbasis of order h. The nonbasis A is maximal if A t3 {b} is an asymptotic LCM basis of order h for every natural number b ¢ A. In this paper the structure of all maximal asymptotic LCM bases of order h is determined.

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