A lower bound for weak Schur numbers with a deterministic algorithm.

Given a positive integer K, the weak Schur problem is to find the largest weakly sum-free K-partition of positive integers. Our goal is to increase known values of n for which the set {1,…,n} can be divided into sum-free sets, i.e. sets for which there are no three distinct elements x, y, z in the same set such that x+y=z.