Divisibility properties of additive bases
Author: Melvyn B. Nathanson
Journal: Proc. Amer. Math. Soc. 96 (1986), 11-14
MSC: Primary 11B99; Secondary 11P99
MathSciNet review: 813799
Abstract: Let . There exists an asymptotic basis of order such that for all if and only if . If , the sumset contains only composite numbers. For , there exists a set of nonnegative integers with for all such that for every prime the sumset contains all sufficiently large multiples of .
Keywords: Density of sumsets, asymptotic bases, additive number theory, additive bases
Article copyright: © Copyright 1986 American Mathematical Society