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On the Order of a Minimal Additive Basis

✍ Scribed by Georges Grekos

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
130 KB
Volume
71
Category
Article
ISSN
0022-314X

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✦ Synopsis

Let A be a set of non-negative integers. If every sufficiently large integer is the sum of h not necessarily distinct elements of A, then A is called an asymptotic basis of order h. An asymptotic basis A of order h is called minimal if no proper subset of A is an asymptotic basis of order h. It is proved that for every integer h 3, no set A is simultaneously a minimal asymptotic basis of orders h and 2h. For h=2, the problem had already been solved.

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