On a board there are $n\geq2$ distinct nonnegative integers such that the sum of each two distinct numbers is a power of $2$. What are the possible values of $n$?
Source: Moldova EGMO TST 2022
Tags: number theory
On a board there are $n\geq2$ distinct nonnegative integers such that the sum of each two distinct numbers is a power of $2$. What are the possible values of $n$?