Erdős problem 868 · problems.science

Let $A$ be an additive basis of order $2$ , let $f(n)$ denote the number of ways in which $n$ can be written as the sum of two elements from $A$ . If $f(n) > \epsilon \log n$ for large $n$ and an arbitrary fixed $\epsilon > 0$ , then must $A$ contain a minimal additive basis of order $2$ ?

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FormalConjectures/ErdosProblems/

868.lean

Retained formal statement4 of 4

Härtter and Nathanson proved that there exist additive bases which do not contain any minimal additive bases.

FormalConjectures/ErdosProblems/868.leanErdos868.erdos_868.variants.Hartter_Nathanson5 linesExact file

1∀ (o : ℕ),2  1 < o →3    ∃ A,4      A.IsAsymptoticAddBasisOfOrder o ∧5        ∀ B ⊆ A, B.IsAsymptoticAddBasisOfOrder o → ∃ b ∈ B, (B \ {b}).IsAsymptoticAddBasisOfOrder o

SolvedStatement only, no proof

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