MathDB

For every positive integer

k

let

a_{k,1},a_{k,2},\ldots

be a sequence of positive integers. For every positive integer

k

let sequence

\{a_{k+1,i}\}

be the difference sequence of

\{a_{k,i}\}

, i.e. for all positive integers

k

and

i

the following holds:

a_{k,i+1}-a_{k,i}=a_{k+1,i}

. Is it possible that every positive integer appears exactly once among numbers

a_{k,i}

?
Proposed by Dávid Matolcsi, Berkeley

Problem Statement