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# Additive bases of positive integers and related problems

Author(s): Artüras Dubickas

Journal: Uniform Distribution Theory
ISSN 1336-913X

Volume: 3;
Issue: 2;
Start page: 81;
Date: 2008;

Keywords: Additive basis | sumset | square of a polynomial.

ABSTRACT
Let $A$ be an infinite set of nonnegativeintegers and let $k \geq 2$ be an integer. We investigate the relation between the number of representations of an integer $n$ by sums of the form $a_1+ \dots+a_k$, where $a_1, \dots, a_k \in A$,and the size of $A$. Some related problems are alsoconsidered.