Erdős problem 476 · problems.science

Let $A\subseteq \mathbb{F}_p$ . Let $A\hat{+}A = \{ a+b : a\neq b \in A\}.$ Is it true that $\lvert A\hat{+}A\rvert \geq \min(2\lvert A\rvert-3,p)?$

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1 retained statement2415f78e850a

FormalConjectures/ErdosProblems/

476.lean

Retained formal statement1 of 1

Let $A\subseteq \mathbb{F}_p$ . Let $A\hat{+}A = \{ a+b : a\neq b \in A\}.$ Is it true that $\lvert A\hat{+}A\rvert \geq \min(2\lvert A\rvert-3,p)?$

This is the Erdős-Heilbronn inequality, proved by Dias da Silva and Hamidoune.

FormalConjectures/ErdosProblems/476.leanErdos476.erdos_4761 lineExact file

1True ↔ ∀ (p : ℕ), Fact (Nat.Prime p) → ∀ (A : Finset (ZMod p)), A.restrictedSumset.card ≥ min (2 * A.card - 3) p

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.