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Erdős problem 785

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Let A,B⊆NA,B\subseteq \mathbb{N} be infinite sets such that A+BA+B contains all large integers. Let A(x)=∣A∩[1,x]∣A(x)=\lvert A\cap [1,x]\rvert and similarly for B(x)B(x). Is it true that if A(x)B(x)∼xA(x)B(x)\sim x then A(x)B(x)−x→∞A(x)B(x)-x\to \infty as x→∞x\to \infty?

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Retained declaration

FormalConjectures/ErdosProblems/785.lean

Formal Conjectures

FormalConjectures/ErdosProblems/785.leanErdos785.erdos_7856 linesExact file
True ↔  ∀ (A B : Set ℕ),    A.Infinite →      B.Infinite →        Erdos785.IsExactAdditiveComplement A B →          Filter.Tendsto (fun x => ↑(Erdos785.counting A x) * ↑(Erdos785.counting B x) - ↑x) Filter.atTop Filter.atTop
SolvedStatement only, no proof

Proof manifests naming this Problem

  • Jayyhk Erdős Leanjayyhk:erdos:785
  • PLBY Lean proofsErdosProblems.Erdos785

Reported activity

Reported by these sources. Not reviewed here.

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