Problem Statement
If $A_1,A_2$ are disjoint additive bases of order $2$ (i.e. $A_i+A_i$ contains all large integers) then must $A=A_1\cup A_2$ contain a minimal additive basis of order $2$ (one such that deleting any element creates infinitely many $n\not\in A+A$)?
Categories:
Number Theory Additive Basis
Progress
A question of Erdős and Nathanson [ErNa88].Härtter [Ha56] and Nathanson [Na74] proved that there exist additive bases which do not contain any minimal additive bases.
Source: erdosproblems.com/869 | Last verified: January 19, 2026