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 $n \neq \in A + A$ )?

Worked, still open.

number theory · solved · 0 attempts

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vela registry pull vfr_37aec80d874a0239

vela reproduce examples/erdos-problems

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unverified AI candidates (2)

gpt-erdos · GPT-5.2 Pro + Deep Research · unverified

As far as I can tell, this is **still open**.

llm-hunter · gpt pro 5.2 · unverified

1 LLM attack(s) recorded (gpt pro 5.2); unverified.

solved