MathDB

Let

b_0, b_1, b_2, \ldots

be a sequence of pairwise distinct nonnegative integers such that

b_0=0

and

b_n<2n

for all positive integers

n

. Prove that for each nonnegative integer

m

there exist nonnegative integers

k, \ell

such that \begin{align*} b_k+b_{\ell}=m. \end{align*}

Problem Statement