# Nonnegative Integers

Problem:

Is it possible to find two subsets A and B of the set of nonnegative integers such that every nonnegative integer x can be written uniquely as a sum x = a + b with a ∈ A, b ∈ B?

Yes. Let A and B be the sets of all nonnegative integers whose binary expansion contains only 0’s at odd (respectively, even) positions, counted from the right.