On arithmetic structures in dense sets of integers

We prove that if A subset of or equal to {1,...,N} has density at least (log log N)(-c), where c is an absolute constant, then A contains a triple (a, a+ d, a +2d) with d = x(2)+y(2) for some integers x, y, not both zero. We combine methods of T Gowers and A. Sarkozy with an application of Selberg's sieve. The result may be regarded as a step toward establishing a fully quantitative version of the polynomial Szemeridi theorem of V. Bergelson and A. Leibman.