Skip to content

Erdős problem 540

Start work

Is it true that if A⊆Z/NZA\subseteq \mathbb{Z}/N\mathbb{Z} has size ≫N1/2\gg N^{1/2} then there exists some non-empty S⊆AS\subseteq A such that ∑n∈Sn≡0(modN)\sum_{n\in S}n\equiv 0\pmod{N}?

No current result

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

Retained declaration

FormalConjectures/ErdosProblems/540.lean

Formal Conjectures

FormalConjectures/ErdosProblems/540.leanErdos540.erdos_5401 lineExact file
True ↔ ∃ C, 0 < C ∧ ∀ (N : ℕ), 0 < N → ∀ (A : Finset (ZMod N)), C * √↑N ≤ ↑A.card → Erdos540.HasZeroSubsetSum A
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:540
  • PLBY Lean proofsErdosProblems.Erdos540

Reported activity

Reported by these sources. Not reviewed here.

Continue

Start a contributionBrowse the source filesOpen the collection entry