On the representation of integers as sums of distinct terms from a fixed set

@inproceedings{Hegyvri2006OnTR,
title={On the representation of integers as sums of distinct terms from a fixed set},
author={Norbert Hegyv{\'a}ri},
year={2006}
}

Introduction. Let A be a strictly increasing sequence of positive integers. The set of all the subset sums of A will be denoted by P (A), i.e. P (A) = {∑ iai : ai ∈ A; i = 0 or 1}. A is said to be subcomplete if P (A) contains an infinite arithmetic progression. A natural question of P. Erdős asked how dense a sequence A which is subcomplete has to be. He conjectured that an+1/an → 1 implies the subcompleteness. But in 1960 J. W. S. Cassels (cf. [1]) showed that for every ε > 0 there exists a… CONTINUE READING