On Sum-Free Arithmetic Sequences

Abstract

An arithmetic sequence of integers is said to be sum-free if no integer of the sequence is the sum of distinct integers of this sequence. This paper investigated whether A = {a, a + d, a + 2d, ...}, where a and d are positive integers, is sum-free, and then showed that there exists a sum-free
subset B of A such that lBl ≥ 1/2 lAl. Moreover, it was also shown that if A = {a, 2a, , T(n) a} , where a is a positive integer, then , where T(n) is the largest positive integer such that A can be partitioned into n sum-free subsets.