On sums and products of integers

Erdos and Szemeredi conjectured that if A is a set of k positive integers, then there must be at least k(2-epsilon) integers that can be written as the sum or product of two elements of A. Erdos and Szemeredi proved that this number must be at least ck(1+delta) for some delta > 0 and k greater than or equal to k(0). In this paper it is proved that the result holds for delta = 1/31.