Problem A6

For a set S of nonnegative integers, let r_S(n) denote the number of ordered pairs (s₁, s₂) such that s₁ Î S, s₂ Î S, s₁ ¹ s₂, and s₁ + s₂ = n. Is it possible to partition the nonnegative integers into two sets A and B in such a way that r_A(n) = r_B(n) for all n?