ON SUBSET SUMS OF R-SETS

A finite set of distinct integers is called an r-set if it contains at least r elements not divisible by q for each q≥2. Let f(n,r) denote the maximum cardinality of an r-set A ⊂ {1,2,...,n} having no subset sum Σεiai(εi=0 or 1, aiε{lunate}A) equal to a power of two. In this paper estimates for f(n,r) are obtained. We prove that limr→∞ αr=0, where αr=limn→∞ f(n,r) n. This result verifies a conjecture of Erdős and Freiman (1990). © 1993.