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Erdős problem 154

Let A⊂{1,…,N}A\subset \{1,\ldots,N\} be a Sidon set with ∣A∣∼N1/2\lvert A\rvert\sim N^{1/2}. Must A+AA+A be well-distributed over all small moduli? In particular, must about half the elements of A+AA+A be even and half odd?

No current result

No reviewed Result is current in Vela Mathematics Program. Retained source material is shown below.

Retained declaration

FormalConjectures/ErdosProblems/154.lean

Formal Conjectures

FormalConjectures/ErdosProblems/154.leanErdos154.erdos_15411 linesExact file
True ↔  ∀ (m : ℕ),    2 ≤ m →      ∀ (N : ℕ → ℕ) (A : ℕ → Finset ℕ),        Filter.Tendsto (fun k => ↑(N k)) Filter.atTop Filter.atTop →          (∀ (k x : ℕ), x ∈ A k → x ≤ N k) →            (∀ (k : ℕ), IsSidon ↑(A k)) →              Filter.Tendsto (fun k => ↑(A k).card / √↑(N k)) Filter.atTop (nhds 1) →                ∀ i < m,                  Filter.Tendsto (fun k => ↑{s ∈ A k + A k | s % m = i}.card / ↑(A k + A k).card) Filter.atTop                    (nhds (1 / ↑m))
SolvedProof has a holelean4external proof

The proof uses `sorry`: part of the argument is written but not proved. Lean accepts the file; it does not accept the theorem.

Proof manifests naming this Problem

  • Jayyhk Erdős Leanjayyhk:erdos:154
  • PLBY Lean proofsErdosProblems.Erdos154
  • William Blair Lean proofswilliamjblair:Erdos154.erdos_154_sumset

Reported activity

Work these sources record against this Problem. Source-reported attribution, not reviewed here.

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