MathDB
2013 ToT Spring Junior A p1 sum of any 2 is some power of 2

Source:

March 4, 2020
number theorypower of 2Sum

Problem Statement

Several positive integers are written on a blackboard. The sum of any two of them is some power of two (for example, 2,4,8,...2, 4, 8,...). What is the maximal possible number of different integers on the blackboard?