MathDB

For a set

S

of nonnegative integers, let

r_S(n)

denote the number of ordered pairs

(s_1, s_2)

such that

s_1 \in S

s_2 \in S

s_1 \neq s_2

, and

s_1 + s_2 = 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

Problem Statement