Følner sequences and sum-free sets

dwi ismayanti;

Erd˝os showed that every set of n positive integers contains a subset of size at least n/(k + 1) containing no solutions to x1 + · · · + xk = y. We prove that the constant 1/(k + 1) here is best possible by showing that if (Fm) is a multiplicative Følner sequence in N, then Fm has no k-sum-free subset of size greater than (1/(k + 1) + o(1))|Fm|.