  We prove a generalisation of Roth's theorem for arithmetic progressions to
d-configurations, which are sets of the form {n_i+n_j+a}_{1 \leq i \leq j \leq
d} where a, n_1,..., n_d are nonnegative integers, using Roth's original
density increment strategy and Gowers uniformity norms. Then we use this
generalisation to improve a result of Sudakov, Szemer\'edi and Vu about
sum-free subsets and prove that any set of n integers contains a sum-free
subset of size at least log n (log log log n)^{1/32772 - o(1)}.
